<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">ADDENDUM: my original message forgot to list my latexmkrcedit, which I should have included rather than, I presume, ~/Library/TeXShop/bin/slatexmk/pdflatexmkrc. Here it is now.<br class=""><div class=""><br class=""></div><div class=""> ============== BEGIN ~/Library/TeXShop/bin/latexmkrcedit ===================</div><div class=""><div class=""># Don't edit this file IF it is named latexmkrcDONTedit directly since</div><div class=""># TeXShop may replace it on update.</div><div class=""># If you wish to edit or add to this file, copy it to ~/Library/TeXShop/bin</div><div class=""># and rename it latexmkrcedit if that file doesn't already exist.</div><div class=""><br class=""></div><div class=""># Edit this File to add/change dependencies and rules</div><div class=""># The following is used by ALL the latexmk engine files</div><div class=""><br class=""></div><div class=""># change '--shell-escape' to an empty string, '', to remove the shell-escape default</div><div class="">#$TSUserCompileOptions = '--shell-escape';</div><div class="">$TSUserCompileOptions = '';</div><div class=""><br class=""></div><div class=""># turn recorder option off (no .fls file generated)</div><div class="">#$recorder=0;</div><div class=""><br class=""></div><div class=""># turn off duplicated missing references</div><div class="">$silence_logfile_warnings = 1;</div><div class=""><br class=""></div><div class=""># Custom dependency for glossaries package</div><div class=""># if you make custom glossaries you may have to add items to the @cus_dep_list and corresponding sub-routines</div><div class=""># NOTE: fileparse and $$Psource are undocumented latexmk as of version 4.40 --- Thanks to John Collins</div><div class=""># if you use the glossary package and DON'T use the glossaries package uncomment (remove the leading #)</div><div class=""># the single line with the system call and comment out (add leading #s) to the two following lines. No</div><div class=""># other changes are necessary. If you use both packages, place any project using the glossary package</div><div class=""># into a folder by itself and create a platexmkrc file containing the lines</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>sub makeglo2gls {</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""># (without the leading #s) in that folder.</div><div class="">add_cus_dep('glo', 'gls', 0, 'makeglo2gls');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makeglo2gls {</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>my ($name, $path) = fileparse($$Psource);</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>return system("makeglossaries -d '$path' '$name'");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""># The glossaries package, with the [acronym] option, produces a .acn file when processed with (xe/pdf)latex and</div><div class=""># then makeindex/xindy to process the .acn into .acr and finally runs of (xe/pdf)latex to read in the .acr file.</div><div class="">add_cus_dep('acn', 'acr', 0, 'makeacn2acr');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makeacn2acr {</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acr '$_[0]'.acn");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>my ($name, $path) = fileparse($$Psource);</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>return system("makeglossaries -d '$path' '$name'");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""># example of an added custom glossary type that is used in some of the glossaries example files:</div><div class=""># this is for the new glossary type command \newglossary[nlg]{notation}{not}{ntn}{Notation} from the glossaries package</div><div class="">add_cus_dep('ntn', 'not', 0, 'makeacn2acr');</div><div class=""># for other glossaries 4.xx examples</div><div class="">add_cus_dep('flo', 'flx', 0, 'makeacn2acr');</div><div class="">add_cus_dep('acn2', 'acr2', 0, 'makeacn2acr');</div><div class=""><br class=""></div><div class=""># the glossary package samples do acr->acn and not->ntn rather than the reverse for the glossaries package</div><div class="">add_cus_dep('acr', 'acn', 0, 'makeacr2acn');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makeacr2acn {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acn '$_[0]'.acr");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class="">add_cus_dep('not', 'ntn', 0, 'makenot2ntn');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makenot2ntn {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.nlg -o '$_[0]'.ntn '$_[0]'.not");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""><br class=""></div><div class=""># dependencies for custom indexes using the index package</div><div class=""># examples for sample.tex for index package:</div><div class=""> add_cus_dep('adx', 'and', 0, 'makeadx2and');</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>sub makeadx2and {</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -o '$_[0]'.and '$_[0]'.adx");</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""> add_cus_dep('ndx', 'nnd', 0, 'makendx2nnd');</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>sub makendx2nnd {</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -o '$_[0]'.nnd '$_[0]'.ndx");</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""> add_cus_dep('ldx', 'lnd', 0, 'makeldx2lnd');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span> sub makeldx2lnd {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span> <span class="Apple-tab-span" style="white-space:pre"> </span> system("makeindex -o '$_[0]'.lnd '$_[0]'.ldx");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span> }</div><div class=""><br class=""></div><div class=""># dependency for biblatex example with a title index</div><div class=""> add_cus_dep('tdx', 'tnd', 0, 'maketdx2tnd');</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>sub maketdx2tnd {</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -o '$_[0]'.tnd '$_[0]'.tdx");</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""><br class=""></div><div class=""># Custom dependency and function for nomencl package</div><div class="">add_cus_dep('nlo', 'nls', 0, 'makenlo2nls');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makenlo2nls {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s nomencl.ist -o '$_[0]'.nls '$_[0]'.nlo");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""><br class=""></div><div class=""># Specify custom index style file:</div><div class="">#$makeindex = "makeindex -s my.ist %O -o %D %S”;</div><div class=""><br class=""></div><div class=""> ============== END ~/Library/TeXShop/bin/latexmkrcedit ===================</div><div class=""><br class=""></div><div><blockquote type="cite" class=""><div class="">On Jul 14, 2017, at 10:45 AM, Murray Eisenberg <<a href="mailto:murrayeisenberg@gmail.com" class="">murrayeisenberg@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta http-equiv="Content-Type" content="text/html charset=utf-8" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">Under macOS Sierra 10.12.5, I upgraded toTeXShop 3.80 from the immediately preceding version, and with the same MacTeX 2017/TeXLive 2017 (except for any TeXLive package updates).<div class=""><br class=""></div><div class="">After updating TeXShop, when I run pdflatexmk on essentially the same complex document (about 300 pages with many source files that are included or inputted, multiple indexes, etc.), it takes many seconds more than it did under the previous version, with noticeable multi-second stops between each run during my single invocation of Typeset with pdflatexmk. </div><div class=""><br class=""></div><div class="">With the previous version, pdflatexmk typesetting ran smoothly, with none of the hiccuping stops now occurring.</div><div class=""><br class=""></div><div class="">My pdflatexmkrc file and contents of the console are listed below. </div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""> =========== BEGIN ~/Library/TewXShop/bin/tslatexmk/pdflatexmkrc =============</div><div class=""><div class=""># Don't edit this file IF it is named latexmkrcDONTedit directly since</div><div class=""># TeXShop may replace it on update.</div><div class=""># If you wish to edit or add to this file, copy it to ~/Library/TeXShop/bin</div><div class=""># and rename it latexmkrcedit if that file doesn't already exist.</div><div class=""><br class=""></div><div class=""># Edit this File to add/change dependencies and rules</div><div class=""># The following is used by ALL the latexmk engine files</div><div class=""><br class=""></div><div class=""># change '--shell-escape' to an empty string, '', to remove the shell-escape default</div><div class="">#$TSUserCompileOptions = '--shell-escape';</div><div class="">$TSUserCompileOptions = '';</div><div class=""><br class=""></div><div class=""># turn recorder option off (no .fls file generated)</div><div class="">#$recorder=0;</div><div class=""><br class=""></div><div class=""># turn off duplicated missing references</div><div class="">$silence_logfile_warnings = 1;</div><div class=""><br class=""></div><div class=""># Custom dependency for glossaries package</div><div class=""># if you make custom glossaries you may have to add items to the @cus_dep_list and corresponding sub-routines</div><div class=""># NOTE: fileparse and $$Psource are undocumented latexmk as of version 4.40 --- Thanks to John Collins</div><div class=""># if you use the glossary package and DON'T use the glossaries package uncomment (remove the leading #)</div><div class=""># the single line with the system call and comment out (add leading #s) to the two following lines. No</div><div class=""># other changes are necessary. If you use both packages, place any project using the glossary package</div><div class=""># into a folder by itself and create a platexmkrc file containing the lines</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>sub makeglo2gls {</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""># (without the leading #s) in that folder.</div><div class="">add_cus_dep('glo', 'gls', 0, 'makeglo2gls');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makeglo2gls {</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>my ($name, $path) = fileparse($$Psource);</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>return system("makeglossaries -d '$path' '$name'");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""># The glossaries package, with the [acronym] option, produces a .acn file when processed with (xe/pdf)latex and</div><div class=""># then makeindex/xindy to process the .acn into .acr and finally runs of (xe/pdf)latex to read in the .acr file.</div><div class="">add_cus_dep('acn', 'acr', 0, 'makeacn2acr');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makeacn2acr {</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acr '$_[0]'.acn");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>my ($name, $path) = fileparse($$Psource);</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>return system("makeglossaries -d '$path' '$name'");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""># example of an added custom glossary type that is used in some of the glossaries example files:</div><div class=""># this is for the new glossary type command \newglossary[nlg]{notation}{not}{ntn}{Notation} from the glossaries package</div><div class="">add_cus_dep('ntn', 'not', 0, 'makeacn2acr');</div><div class=""># for other glossaries 4.xx examples</div><div class="">add_cus_dep('flo', 'flx', 0, 'makeacn2acr');</div><div class="">add_cus_dep('acn2', 'acr2', 0, 'makeacn2acr');</div><div class=""><br class=""></div><div class=""># the glossary package samples do acr->acn and not->ntn rather than the reverse for the glossaries package</div><div class="">add_cus_dep('acr', 'acn', 0, 'makeacr2acn');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makeacr2acn {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acn '$_[0]'.acr");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class="">add_cus_dep('not', 'ntn', 0, 'makenot2ntn');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makenot2ntn {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.nlg -o '$_[0]'.ntn '$_[0]'.not");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""><br class=""></div><div class=""># dependencies for custom indexes using the index package</div><div class=""># examples for sample.tex for index package:</div><div class=""> add_cus_dep('adx', 'and', 0, 'makeadx2and');</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>sub makeadx2and {</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -o '$_[0]'.and '$_[0]'.adx");</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""> add_cus_dep('ndx', 'nnd', 0, 'makendx2nnd');</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>sub makendx2nnd {</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -o '$_[0]'.nnd '$_[0]'.ndx");</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""> add_cus_dep('ldx', 'lnd', 0, 'makeldx2lnd');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span> sub makeldx2lnd {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span> <span class="Apple-tab-span" style="white-space:pre"> </span> system("makeindex -o '$_[0]'.lnd '$_[0]'.ldx");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span> }</div><div class=""><br class=""></div><div class=""># dependency for biblatex example with a title index</div><div class=""> add_cus_dep('tdx', 'tnd', 0, 'maketdx2tnd');</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>sub maketdx2tnd {</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -o '$_[0]'.tnd '$_[0]'.tdx");</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""><br class=""></div><div class=""># Custom dependency and function for nomencl package</div><div class="">add_cus_dep('nlo', 'nls', 0, 'makenlo2nls');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makenlo2nls {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s nomencl.ist -o '$_[0]'.nls '$_[0]'.nlo");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""><br class=""></div><div class=""># Specify custom index style file:</div><div class="">#$makeindex = "makeindex -s my.ist %O -o %D %S";# Don't edit this file IF it is named latexmkrcDONTedit directly since</div><div class=""># TeXShop may replace it on update.</div><div class=""># If you wish to edit or add to this file, copy it to ~/Library/TeXShop/bin</div><div class=""># and rename it latexmkrcedit if that file doesn't already exist.</div><div class=""><br class=""></div><div class=""># Edit this File to add/change dependencies and rules</div><div class=""># The following is used by ALL the latexmk engine files</div><div class=""><br class=""></div><div class=""># change '--shell-escape' to an empty string, '', to remove the shell-escape default</div><div class="">#$TSUserCompileOptions = '--shell-escape';</div><div class="">$TSUserCompileOptions = '';</div><div class=""><br class=""></div><div class=""># turn recorder option off (no .fls file generated)</div><div class="">#$recorder=0;</div><div class=""><br class=""></div><div class=""># turn off duplicated missing references</div><div class="">$silence_logfile_warnings = 1;</div><div class=""><br class=""></div><div class=""># Custom dependency for glossaries package</div><div class=""># if you make custom glossaries you may have to add items to the @cus_dep_list and corresponding sub-routines</div><div class=""># NOTE: fileparse and $$Psource are undocumented latexmk as of version 4.40 --- Thanks to John Collins</div><div class=""># if you use the glossary package and DON'T use the glossaries package uncomment (remove the leading #)</div><div class=""># the single line with the system call and comment out (add leading #s) to the two following lines. No</div><div class=""># other changes are necessary. If you use both packages, place any project using the glossary package</div><div class=""># into a folder by itself and create a platexmkrc file containing the lines</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>sub makeglo2gls {</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""># (without the leading #s) in that folder.</div><div class="">add_cus_dep('glo', 'gls', 0, 'makeglo2gls');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makeglo2gls {</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>my ($name, $path) = fileparse($$Psource);</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>return system("makeglossaries -d '$path' '$name'");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""># The glossaries package, with the [acronym] option, produces a .acn file when processed with (xe/pdf)latex and</div><div class=""># then makeindex/xindy to process the .acn into .acr and finally runs of (xe/pdf)latex to read in the .acr file.</div><div class="">add_cus_dep('acn', 'acr', 0, 'makeacn2acr');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makeacn2acr {</div><div class="">#<span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acr '$_[0]'.acn");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>my ($name, $path) = fileparse($$Psource);</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>return system("makeglossaries -d '$path' '$name'");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""># example of an added custom glossary type that is used in some of the glossaries example files:</div><div class=""># this is for the new glossary type command \newglossary[nlg]{notation}{not}{ntn}{Notation} from the glossaries package</div><div class="">add_cus_dep('ntn', 'not', 0, 'makeacn2acr');</div><div class=""># for other glossaries 4.xx examples</div><div class="">add_cus_dep('flo', 'flx', 0, 'makeacn2acr');</div><div class="">add_cus_dep('acn2', 'acr2', 0, 'makeacn2acr');</div><div class=""><br class=""></div><div class=""># the glossary package samples do acr->acn and not->ntn rather than the reverse for the glossaries package</div><div class="">add_cus_dep('acr', 'acn', 0, 'makeacr2acn');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makeacr2acn {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acn '$_[0]'.acr");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class="">add_cus_dep('not', 'ntn', 0, 'makenot2ntn');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makenot2ntn {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s '$_[0]'.ist -t '$_[0]'.nlg -o '$_[0]'.ntn '$_[0]'.not");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""><br class=""></div><div class=""># dependencies for custom indexes using the index package</div><div class=""># examples for sample.tex for index package:</div><div class=""> add_cus_dep('adx', 'and', 0, 'makeadx2and');</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>sub makeadx2and {</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -o '$_[0]'.and '$_[0]'.adx");</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""> add_cus_dep('ndx', 'nnd', 0, 'makendx2nnd');</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>sub makendx2nnd {</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -o '$_[0]'.nnd '$_[0]'.ndx");</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""> add_cus_dep('ldx', 'lnd', 0, 'makeldx2lnd');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span> sub makeldx2lnd {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span> <span class="Apple-tab-span" style="white-space:pre"> </span> system("makeindex -o '$_[0]'.lnd '$_[0]'.ldx");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span> }</div><div class=""><br class=""></div><div class=""># dependency for biblatex example with a title index</div><div class=""> add_cus_dep('tdx', 'tnd', 0, 'maketdx2tnd');</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>sub maketdx2tnd {</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -o '$_[0]'.tnd '$_[0]'.tdx");</div><div class=""> <span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""><br class=""></div><div class=""># Custom dependency and function for nomencl package</div><div class="">add_cus_dep('nlo', 'nls', 0, 'makenlo2nls');</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>sub makenlo2nls {</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>system("makeindex -s nomencl.ist -o '$_[0]'.nls '$_[0]'.nlo");</div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>}</div><div class=""><br class=""></div><div class=""># Specify custom index style file:</div><div class="">#$makeindex = "makeindex -s my.ist %O -o %D %S”;</div></div><div class=""><br class=""></div><div class=""> =========== END ~/Library/TewXShop/bin/tslatexmk/pdflatexmkrc =============</div><div class=""><br class=""></div><div class=""> =========== BEGIN console file ===============</div><div class=""><br class=""></div><div class=""> <span style="font-family: Monaco; font-size: 11px;" class="">Subroutine makeglo2gls redefined at (eval 9) line 2, <GEN2> chunk 1.</span></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: This is Latexmk, John Collins, 16 May 2017, version: 4.53a.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'pdflatex': Rules & subrules not known to be previously run:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> pdflatex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'pdflatex': The following rules & subrules became out-of-date:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'pdflatex'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 1 of rule 'pdflatex'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'pdflatex --synctex=1 --file-line-error -recorder "topologybook.tex"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'pdflatex'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017) (preloaded format=pdflatex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> restricted \write18 enabled.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">entering extended mode</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX2e <2017-04-15></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Babel <3.12> and hyphenation patterns for 84 language(s) loaded.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/snapshot/snapshot.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/memoir.cls</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Document Class: memoir 2016/05/16 v3.7f configurable book, report, article docu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ment class</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ifpdf.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/scalerel/scalerel.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/my/mywidebar.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/my/myaccents.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Using mymath variant defs for Lucida Bright.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Using mymath variant defs for Lucida Bright.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (/Users/murray/Library/texmf/tex/generic/diagxy/diagxy.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xy.tex Bootstrap'ing:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">catcodes, docmode,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyrecat.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyidioms.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic version 3.8.9 <2013/10/06></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Copyright (c) 1991-2013 by Kristoffer H. Rose <<a href="mailto:krisrose@tug.org" class="">krisrose@tug.org</a>> and others</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic is free software: see the User's Guide for details.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Loading kernel: messages; fonts; allocations: state, direction,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">utility macros; pictures: \xy, positions, objects, decorations;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">kernel objects: directionals, circles, text; options; algorithms: directions,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">edges, connections; Xy-pic loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyarrow.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic option: Arrow and Path feature v.3.9 path, \ar, loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xycurve.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic option: Curve and Spline extension v.3.12 curve, circles, loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucida/t1hlh.fd))) (./preamble/style.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-patch.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/parseargs.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-kv.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/infwarerr.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/etexcmds.sty)))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-autoref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/aliasctr.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/carlisle/remreset.sty)))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-listof.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-restate.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-amsthm.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">****************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Made patch specific for amsthm.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">****************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./preamble/links.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/biblatex.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ltxcmds.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/kvoptions.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/logreq/logreq.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/logreq/logreq.def))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/url/url.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/blx-dm.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/blx-compat.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/blx-bibtex.def</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Using fall-back BibTeX(8) backend:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) functionality may be reduced/unavailable.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/biblatex.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/biblatex/bbx/mybooknumeric.bbx</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/bbx/standard.bbx)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/bbx/numeric.bbx))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/cbx/numeric.cbx)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./biblatex.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/nomencl/nomencl.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Using the configuration file nomencl.cfg</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./nomencl.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/repeatindex/repeatindex.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/tools/afterpage.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/hyperref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/auxhook.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/pd1enc.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/latexconfig/hyperref.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/memhfixc.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Message: Driver (autodetected): hpdftex.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/hpdftex.def</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Option `pdftex' has already been used,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) setting the option has no effect on input line 107.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/xmpincl/xmpincl.sty)<<TopologyEd2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">metadata.xmpi>></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperxmp/hyperxmp.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/stringenc.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/doclicense/doclicense.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/xifthen/xifthen.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/tools/xspace.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/doclicense/doclicense-english.ldf</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) (/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/aliascnt.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/cleveref/cleveref.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./preamble/labels.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/showlabels/showlabels.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package: `showlabels' v1.8 <2016/06/09></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">with amsmath equation tags</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">))) (/usr/local/texlive/2017/texmf-dist/tex/latex/microtype/microtype.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/microtype/microtype-pdftex.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/microtype/microtype.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing nomenclature file topologybook.nlo</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing index file notation.idx </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing index file names.idx </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing index file topologybook.idx </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/biblatex/lbx/mylanguagestrings.lbx</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/lbx/english.lbx))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/ccicons/ccicons.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/xkeyval/xkeyval.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xkeyval/xkeyval.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xkeyval/xkvutils.tex))))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/base/ts1cmr.fd)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/cyrillic/ot2cmr.fd)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/context/base/mkii/supp-pdf.mkii</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[Loading MPS to PDF converter (version 2006.09.02).]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/grfext.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ABD: EveryShipout initializing macros</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file topologybook.bbl.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/nameref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/gettitlestring.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Redoing nameref's sectioning</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Redoing nameref's label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/se-pdfdoc.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/se-utf8.def) [1{/Users</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/murray/Library/texlive/2017/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[2] [3] [4] (./main/mainmatter.tex (./main/SetsMaps/chapterSetsMaps.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/setsmaps-init.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'EisenbergMathMethod1996' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 11.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'LakinsMathReasoning2016' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 12.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'PinterSets2014' on page 1 undefined on input line 13.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'BourbakiSets2004' on page 1 undefined on input line 15</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'EisenbergSets1971' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">6.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'Bernays1991' on page 1 undefined on input line 17.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'Suppes1972' on page 1 undefined on input line 20.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (75.8248pt too wide) in paragraph at lines 8--24</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) for ex-am-ple, Eisen-berg [[]], Lakins [[]],</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (25.4927pt too wide) in paragraph at lines 8--24</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) [[]] (or, with a dif-fer-ent ax-iomatic foun-da-tion, Sup-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pes [[]]). </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/SetsMaps/logic.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 3492) has occurred while \output is active [1])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/sets.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:finite' on page 1 undefined on input line 65.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:finite' on page 1 undefined on input line 65.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[2]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:predicate-logic' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 72.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[3]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:maps' on page 1 undefined on input line 104.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:intervals' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">12.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:Russell-paradox' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 116.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[4]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:intervals' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">96.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:intervals' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">96.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[5]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:def-equal-sets' on page 6 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">260.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:def-equal-sets' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">260.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:def-subset' on page 6 undefined on input line 260.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:def-subset' on page 1 undefined on input line 260.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:both-element-and-subset' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 273.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[6] (/Users/murray/Library/texmf/tex/latex/lucidabr/omshlh.fd)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `axiom:induction' on page 7 undefined on input line 35</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">4.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `axiom:induction' on page 7 undefined on input line 35</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">4.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[7]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:wo' on page 1 undefined on input line 369.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `axiom:induction' on page 8 undefined on input line 40</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `axiom:induction' on page 8 undefined on input line 40</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1418) has occurred while \output is active [8]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[9]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:families' on page 1 undefined on input line 526.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[10]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:tuples-sequences' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 579.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:tuples-sequences' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 579.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[11]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:maps' on page 1 undefined on input line 646.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:order-relations' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 652.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:equiv' on page 1 undefined on input line 658.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[12]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:types-of-relations' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 728.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (38.67267pt too wide) in paragraph at lines 733--734</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) verse re-la-tion $[]$ is \T1/hlh/m/it/10 (-20) not \T1/hlh</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/m/n/10 (-20) func-tional be-cause the set $\OMS/hlcy/m/n/10 f [] g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[13]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:union-intersect-nil-nest' on page 14 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 810.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:powersets-nil-nest' on page 14 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 810.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[14]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:wo-principle' on page 15 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">926.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:wo-principle' on page 15 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">926.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `axiom:induction' on page 15 undefined on input line 9</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">26.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `axiom:induction' on page 15 undefined on input line 9</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">26.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/SetsMaps/maps.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:relations' on page 1 undefined on input line 3</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">5.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[15]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:closed-graph-no-compact' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 55.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:graph-closed-if-continuous' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 55.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[16] [17] [18] [19]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `add-assoc' on page 20 undefined on input line 328.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `add-negs' on page 20 undefined on input line 328.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `mult-assoc' on page 20 undefined on input line 328.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `mult-recip' on page 20 undefined on input line 328.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `distrib' on page 20 undefined on input line 328.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `add-cancel' on page 20 undefined on input line 357.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `mult-cancel' on page 20 undefined on input line 357.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `add-assoc' on page 20 undefined on input line 357.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `add-negs' on page 20 undefined on input line 357.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `mult-assoc' on page 20 undefined on input line 357.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `mult-recip' on page 20 undefined on input line 357.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `distrib' on page 20 undefined on input line 357.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[20] [21]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:extend-many-pieces' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 502.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[22] [23] [24]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:direct-and-inverse-image' on page 1 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 694.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `problem-part:image-intersection-strict' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 694.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[25] [26]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:prove-composite-inj-surj-implies-one-is' on page</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1 undefined on input line 835.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:inj-implies-exists-retraction' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 863.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-part:exists-retraction-implies-inj' on page 27 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 863.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:surj-implies-exists-section' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 864.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-part:exists-section-implies-surj' on page 27 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 864.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[27]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:reverse-relation' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 901.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:composite-inj-surj-implies-one-is' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 919.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[28]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:two-bijections' on page 29 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 934.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:inj-surj-bij' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 934.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:inj-surj-bij' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 934.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:inverse-of-inverse' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 934.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:prove-inverse-map-properties' on page 1 undefine</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">d on input line 970.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[29] [30]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eqn:direct-inverse-images' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1110.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:composite-inj-surj-implies-one-is' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 1148.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:section-and-retraction-implies-inj-surj' on page </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1 undefined on input line 1154.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-part:exists-retraction-implies-inj' on page 31 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 1154.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[31]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:inverse-map-properties' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 1165.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/SetsMaps/families.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 48.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 48.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[32]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 116.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 116.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[33] [34] [35] [36]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:union-intersect-two' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 368.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:union-intersect-two' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 368.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:union-intersect-two' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 373.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:DeMorgans-laws' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">399.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[37]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eqn:direct-inverse-images' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 443.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:extend-two-pieces' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 445.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[38]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:extend-two-pieces' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 469.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[39]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:ordered-pairs' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 564.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:ordered-pairs' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 564.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:composite' on page 1 undefined on input line 5</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">82.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:composite' on page 1 undefined on input line 5</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">82.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[40] [41]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:power-of-set' on page 1 undefined on input line 6</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">61.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:nth-power-of-set' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 670.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:nth-power-of-set' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 670.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:finite-product-nonempty' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 687.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[42]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-function' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 718.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-set' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">728.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:AC-equivalents' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 730.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:inf-set-has-den-subset' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 732.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[43]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:extend-many-pieces' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 859.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:union-intersect-collection' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 900.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[44]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.57535pt too wide) in paragraph at lines 909--910</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Let $\OML/hlcm/m/it/10 n$ \T1/hlh/m/n/10 (-20) be a pos-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">i-tive in-te-ger and let $\OML/hlcm/m/it/10 ÑX[]Ö[]$ \T1/hlh/m/n/10 (-20) be a </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fam-ily of \T1/hlh/m/it/10 (-20) nonempty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:section-and-retraction-implies-inj-surj' on page </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1 undefined on input line 938.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-part:exists-section-implies-surj' on page 45 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 938.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ax:AC' on page 45 undefined on input line 946.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-product' on page 45 undefined on input line 94</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">6.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-function' on page 45 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 946.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-set' on page 45 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 946.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ax:AC' on page 45 undefined on input line 951.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-function' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 951.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-set' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">951.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-function' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 954.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ax:AC' on page 45 undefined on input line 954.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ax:AC' on page 45 undefined on input line 957.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-function' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 957.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/SetsMaps/recursion.tex [45] [46]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-eq:IC-and-recurrence' on page 47 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 99.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq:recurse-2' on page 47 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">32.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:extend-many-pieces' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 136.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq:recurse-1' on page 47 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">44.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-eq:IC-and-recurrence' on page 47 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 144.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[47]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq:recurse-4' on page 48 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">83.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[48]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:ordinary-recursion' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 222.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:ordinary-recursion' on page 49 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 242.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:ordinary-recursion' on page 49 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 242.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:ordinary-recursion' on page 49 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 246.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:ordinary-recursion' on page 49 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 246.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:ordinary-recursion' on page 49 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 291.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:ordinary-recursion' on page 49 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 291.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[49]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-eq-primitive-recurse' on page 50 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 320.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq-primitive-recurse-3' on page 50 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 341.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq-primitive-recurse-4' on page 50 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 368.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:ordinary-recursion' on page 50 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 368.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:ordinary-recursion' on page 50 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 368.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[50]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq-primitive-recurse-2' on page 51 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 373.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq-primitive-recurse-3' on page 51 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 378.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq-primitive-recurse-1' on page 51 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 384.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq-primitive-recurse-5' on page 51 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 384.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq-primitive-recurse-3' on page 51 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 384.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq-primitive-recurse-6' on page 51 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 384.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-eq-primitive-recurse' on page 51 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 403.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:ordinary-recursion' on page 51 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 411.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:primitive-recursion' on page 51 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 413.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:complete-recursion' on page 51 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 441.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:inf-subset-of-countable' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 441.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[51]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:union-intersection-family' on page 1 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 520.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[52]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:ordinary-recursion' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 549.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:primitive-recursion' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 549.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:complete-recursion' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 549.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:complete-recursion' on page 53 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 566.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:complete-recursion' on page 53 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 566.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/SetsMaps/countable.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:one-one-corr' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[53]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.3389pt too wide) in paragraph at lines 84--88</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) Hence the map ob-tained from $\OML/hlcm/m/it/10 h[]$ \T1/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lh/m/n/10 (-20) by re-strict-ing its do-main to $\OMS/hlcy/m/n/10 f\T1/hlh/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ; n;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> n \OMS/hlcy/m/n/10 Ç</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:union-finite-family-of-finite-sets' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 99.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[54]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.72176pt too wide) in paragraph at lines 152--155</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Now let $\OML/hlcm/m/it/10 n \OMS/hlcy/m/n/10 ^^U \T1/hl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">h/m/n/10 (-20) 1$ and as-sume that each sub-set of $\OMS/hlcy/m/n/10 f\T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> n\OMS/hlcy/m/n/10 g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:disj-union-finite-sets' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 158.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:N-is-infinite' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">71.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[55]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:subset-of-finite' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 191.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:disj-union-finite-sets' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 191.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:union-finite-family-of-finite-sets' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 240.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:union-finite-family-of-finite-sets' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 243.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[56]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:wo-principle' on page 57 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">258.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:wo-principle' on page 57 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">258.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:subset-of-finite' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 284.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[57]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:subset-of-finite' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 345.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:inf-subset-of-countable' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 372.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:N-is-infinite' on page 1 undefined on input line 3</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">74.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:subset-of-finite' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 374.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[58]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:complete-recursion' on page 59 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 394.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:complete-recursion' on page 59 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 394.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-function' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 394.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:image-of-finite-set' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 406.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:image-of-countable-set' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 417.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-eq:two-three-powers' on page 59 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 448.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[59]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:image-of-countable-set' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 485.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:N-times-N-denumerable' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 485.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:countable-union-of-countable-sets' on page 1 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 491.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:Z-is-denumerable' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 496.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:product-finite-family-countable-sets' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 519.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[60] [61]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:uncountable-product-of-doubletons' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 586.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:reals-uncountable' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 587.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:N-is-infinite' on page 1 undefined on input line 6</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">18.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[62]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:poly-for-algebraic' on page 63 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 724.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[63]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:inf-set-has-den-subset' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 755.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-function' on page 64 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 755.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-function' on page 64 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 755.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-function' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 755.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/SetsMaps/ordering.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:antisymmetric' on page 64 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 66.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:partial-order' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">66.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:comparable' on page 64 undefined on input line 66</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:comparable' on page 1 undefined on input line 66.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[64] [65] [66]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 67 undefined on input line 292.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:preorderings' on page 1 undefined on input line 29</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">2.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:preorder-on-subset' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 292.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:divisibility-po' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 296.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[67] [68]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 69 undefined on input line 398.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:partial-orders' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">398.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:inclusion-po' on page 1 undefined on input line 39</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">8.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[69] [70]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:intervals-in-R' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 552.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[71] [72] [73]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:dictionary-order' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 733.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[74]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 75 undefined on input line 768.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:partial-orders' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">768.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:divisibility-po' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 768.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[75] [76]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:upper-bound-property-of-direction' on page 77 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 907.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:dictionary-order' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 956.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 77 undefined on input line 961.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:partial-orders' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">961.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:product-ordering' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 961.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 77 undefined on input line 966.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:partial-orders' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">966.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:product-ordering' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 966.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[77] [78]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:preorder-is-generated-like-that' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 1050.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:generate-preorder-from-surj' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 1055.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:equiv' on page 1 undefined on input line 1056.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:generate-preorder-from-surj' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 1086.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/SetsMaps/ordercomplete.tex [79]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ax:R-order-complete' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 55.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[80] [81]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:closed-interval-R-uncountable' on page 1 undefine</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">d on input line 200.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:interval' on page 1 undefined on input line 214.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `txt:std-intervals' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">226.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[82]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pfcase:all-intervals-lower-not-upper-bound' on page 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> undefined on input line 275.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/SetsMaps/equivrel.tex [83]) (./main/SetsMaps/well-ordering.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:comparable' on page 84 undefined on input line 19</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:wo-principle' on page 84 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">20.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:wo-principle' on page 84 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">20.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:1st-uncountable-ordinal' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 44.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:1st-uncountable-ordinal' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 44.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[84]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:wo-principle' on page 85 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">63.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:wo-principle' on page 85 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">63.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf:OmegaPlus-exists' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 100.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:OmegaPlus4' on page 85 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 109.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:OmegaPlus1' on page 85 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 111.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:OmegaPlus4' on page 85 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 111.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[85]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:bded-above-subset-wo-has-sup' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 158.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:sups-exist-in-OmegaPlus' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 167.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:bded-above-subset-wo-has-sup' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 180.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:OmegaPlus4' on page 86 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 183.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:OmegaPlus-exists' on page 86 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 226.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:OmegaPlus-exists' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 226.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-wo' on page 86 undefined on input line 226.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-wo' on page 86 undefined on input line 226.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:OmegaPlus-exists' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 230.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:dictionary-order' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 239.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:dictionary-order-product-wo' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 240.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[86]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:OmegaPlus1' on page 87 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 257.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:OmegaPlus4' on page 87 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 257.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[87]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 300.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-wo' on page 1 undefined on input line 319.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'KneserZorn1950' on page 88 undefined on input line 322</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'GraysonZorn2007' on page 88 undefined on input line 32</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">5.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'GaillardZorn2017' on page 88 undefined on input line 3</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">25.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[88]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ax:AC' on page 89 undefined on input line 405.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ax:AC' on page 89 undefined on input line 405.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf:zorn-step-1' on page 1 undefined on input line 409</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[89]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:star-zorn-pf' on page 90 undefined on input line 4</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">83.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf:zorn-step-5' on page 1 undefined on input line 523</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-zorn-claim-a' on page 90 undefined on input line 5</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">23.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[90]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf:zorn-step-6' on page 1 undefined on input line 577</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:zorn-prelim-lemma' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 577.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:zorn-prelim-lemma' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 590.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:star-zorn-pf' on page 91 undefined on input line 5</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">90.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:star-zorn-pf' on page 1 undefined on input line 59</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:zorn-prelim-lemma' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 590.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:star-zorn-pf' on page 91 undefined on input line 5</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">90.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:star-zorn-pf' on page 1 undefined on input line 59</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[91]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 619.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-wo-cond-i' on page 92 undefined on input line 670.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-wo-cond-ii' on page 92 undefined on input line 671</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[92]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-wothm-same-i' on page 93 undefined on input line 6</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">92.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-wothm-S-and-Ri' on page 93 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 692.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-wo-cond-ii' on page 93 undefined on input line 695</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-wothm-same-i' on page 93 undefined on input line 6</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">97.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-wothm-S-and-Ri' on page 93 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 697.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-wothm-S-and-Ri' on page 93 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 703.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-wo-cond-i' on page 93 undefined on input line 704.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-wo-cond-ii' on page 93 undefined on input line 704</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `pf-wothm-S-and-Ri' on page 93 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 705.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ZornLemma' on page 93 undefined on input line 712.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ZornLemma' on page 93 undefined on input line 712.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.15701pt too wide) in paragraph at lines 727--728</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) The pre-ced-ing proof is a typ-i-cal pro-ce-dure for ap-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ply-ing Zorn's Lemma.To</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:wo' on page 1 undefined on input line 782.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:dictionary-order' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 787.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[93]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:extend-wo-to-greatest-elt' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 816.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:transfinite-induction' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 845.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-cond-trans-induct-hyp' on page 94 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 847.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 94 undefined on input line 856.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:partial-orders' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">856.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:divisibility-po' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 856.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[94]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:of-finite-character' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 922.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (14.17062pt too wide) in paragraph at lines 922--932</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) Continuation of [].\T1/hlh/m/n/10</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> (-20) ) Prove the \T1/hlh/b/n/10 Teichm¸ller-Tukey Lemma\T1/hlh/m/n/10 (-20) :</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> A nonempty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:AC-choice-function' on page 95 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 934.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) [95] (./main/MetricSpaces/chapterMetrics.tex [96]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/MetricSpaces/metrics-init.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:compactmetric' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">23.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:compact' on page 1 undefined on input line 23.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/MetricSpaces/metrics.tex [97]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.58485pt too wide) in paragraph at lines 79--79</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[98]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:translation-rotation-invariant-metrics' on page </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1 undefined on input line 120.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:euclidean-spaces' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 122.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:euclidean-spaces' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 122.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[99]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem-part:norm-nonneg' on page 100 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 179.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem-part:norm-strict-pos' on page 100 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 179.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem-part:norm-strict-pos' on page 100 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 179.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[100] [101]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:CS-inequality' on page 102 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 270.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:CS-inequality' on page 102 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 270.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:norm-properties' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 270.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:norm-properties' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 288.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:norm-properties' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 327.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem-part:norm-strict-pos' on page 102 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 327.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (4.21518pt too wide) in paragraph at lines 327--329</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Since $\OML/hlcm/m/it/10 dÑx; yÖ \OMS/hlcy/m/n/10 É k\OM</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">L/hlcm/m/it/10 x \OMS/hlcy/m/n/10 ^^@ \OML/hlcm/m/it/10 y\OMS/hlcy/m/n/10 k$\T1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/hlh/m/n/10 (-20) , then from [] [] we have $\OML/hlcm/m/it/10 dÑx; yÖ \OMS/hlc</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">y/m/n/10 É</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:norm-properties' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 331.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem-part:norm-homog' on page 102 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 331.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[102]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:norm-properties' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 338.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem-part:norm-triangle' on page 103 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 338.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:Euclidean-d-properties' on page 103 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 356.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:Euclidean-d-stric-pos' on page 103 undefine</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">d on input line 356.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:Euclidean-d-properties' on page 103 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 357.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:Euclidean-d-symmetric' on page 103 undefine</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">d on input line 357.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:Euclidean-d-properties' on page 103 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 358.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:Euclidean-d-triangle' on page 103 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 358.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:triangle-inequality' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 361.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `superscript' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[103]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:taxicab-dist' on page 1 undefined on input line 3</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">78.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.6}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.384 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:taxicab-metric}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:Euclidean-d-properties' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 406.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[104] [105]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:dmax-stric-pos' on page 106 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 501.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:dmax-triangle' on page 106 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 501.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucida/ts1hlh.fd)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:translation-rotation-invariant-metrics' on page </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1 undefined on input line 522.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:metrics-and-metric-spaces' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 528.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:metrics-and-metric-spaces' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 528.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[106]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:extreme-value-thm' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 548.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:max-metric-dist-fns' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 563.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:max-metric' on page 1 undefined on input line 571</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[107]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:dmax-fns-triangle' on page 108 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 597.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (9.80023pt too wide) in paragraph at lines 624--625</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hls/b/n/10 1.9 Ex-am-ple. []\T1/hlh/m/n/10 (-20) Again let $\OML/hlcm/m/i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t/10 X$ \T1/hlh/m/n/10 (-20) be the set of all con-tin-u-ous func-tions $\OML/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lcm/m/it/10 x [] [] Ü\T1/hlh/m/n/10 (-20) 0\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-20) 1\OML/hlcm/m/it/10 á [] \LMR/hlcm/m/n/10 R$\T1/hlh/m/n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:d1-dist-between-functions' on page 1 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 630.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:d1-fns-stric-pos' on page 108 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 668.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[108] [109] [110]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:norm-properties' on page 111 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 763.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem-part:norm-triangle' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 763.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 111 undefined on input line 773.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:seq-conv-metric' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 773.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:seq-nonneg-conv-iff-partial-sums-bded-above' on pa</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ge 1 undefined on input line 773.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:norm-properties' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 801.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:Euclidean-d-properties' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 803.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[111] [112]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:max-metric' on page 1 undefined on input line 970</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:generalize-d-and-d1-to-product' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 971.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[113]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1014.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:metrics-fn-and-seq-spaces' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 1015.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:metrics-fn-and-seq-spaces' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 1015.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:norm-properties' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1040.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Hyper reference `lem:CS-inequality' on page 114 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1040.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:CS-inequality' on page 114 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1040.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[114]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.90543pt too wide) in paragraph at lines 1092--1093</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Are the taxi-cab and max met-rics on $\LMR/hlcm/m/n/10 R</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]$ \T1/hlh/m/n/10 (-20) also translation-invariant?</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1098.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[115]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:max-metric-on-product' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 1153.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:metric-on-seq-bded-metric-spaces' on page 1 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 1198.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:base-dprime-denumerable-product' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 1198.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:norm-properties' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1212.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[116]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:pseudometric' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1256.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:metric-nonnegative' on page 117 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 1292.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:metric-symmetric' on page 117 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 1292.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[117]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:UM' on page 118 undefined on input line 1309</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sequence-space-metric' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 1313.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:p-adic-metric' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1316.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:p-adic-norm' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">316.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:ultametric-bis' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1317.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:ultrametric' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">331.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[118]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:p-adic-norm' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">416.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:ultrametric' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">443.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/MetricSpaces/openclosed.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:contconv' on page 1 undefined on input line 16.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[119]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:pt-inside-sphere-on-segment' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 102.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:pt-inside-sphere-on-segment' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 102.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[120]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:ball-in-R1' on page 1 undefined on input line 108</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:ball-in-R2' on page 1 undefined on input line 122</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:ball-in-R3' on page 1 undefined on input line 136</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `inlinedef:convex' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">47.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:norm-properties' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 153.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[121] [122]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:max-metric' on page 1 undefined on input line 213</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:ball-for-max-metric' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 228.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[123]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:discrete-metric' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 240.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:induced-d' on page 1 undefined on input line 255.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sup-metric-on-functions' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 266.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[124]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:ball-in-C-unit-interval' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 291.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:small-ball-inside-ball' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 305.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[125]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:small-ball-inside-ball' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 339.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[126]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:spaces' on page 1 undefined on input line 420.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:discrete-metric' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 432.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:open-sets-properties-in-metric-space' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 432.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[127]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:intervals-in-R' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 467.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:open-sets-properties-in-metric-space' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 477.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:union-of-d-open-sets-is-d-open' on page 128 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">undefined on input line 477.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:open-interval-ray-d-open' on page 128 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 477.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[128]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:interval' on page 1 undefined on input line 530.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[129]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:induced-d' on page 1 undefined on input line 568.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:d-prime-open-in-subset' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 574.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:open-intersect-subset-metric' on page 130 undefine</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">d on input line 589.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:open-sets-properties-in-metric-space' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 597.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:union-of-d-open-sets-is-d-open' on page 130 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">undefined on input line 597.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[130]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:all-d-open-sets-in-R' on page 131 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 607.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:open-sets-subset-metric' on page 131 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 607.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [131]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:open-sets-properties-in-metric-space' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 692.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[132]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:open-sets-properties-in-metric-space' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 724.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:nil-and-whole-are-d-open' on page 1 undefine</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">d on input line 724.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:DeMorgans-laws' on page 133 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 734.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:DeMorgans-laws' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 734.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:DeMorgans-laws' on page 133 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 734.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:DeMorgans-laws' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 734.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:open-sets-properties-in-metric-space' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 735.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:union-of-d-open-sets-is-d-open' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 735.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:union-of-finitely-many-d-closed-sets-is-d-cl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">osed' on page 133 undefined on input line 738.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:union-of-finitely-many-d-closed-sets-is-d-cl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">osed' on page 1 undefined on input line 738.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:open-sets-properties-in-metric-space' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 738.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:connected' on page 1 undefined on input line 753</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[133]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:ball-disk-disjoint' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 785.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:closed-sets-properties-in-metric-space' on page 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> undefined on input line 798.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:union-of-finitely-many-d-closed-sets-is-d-cl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">osed' on page 1 undefined on input line 798.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:separation-axioms' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 800.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def-item:T1' on page 134 undefined on input line 800.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1178) has occurred while \output is active [134]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:separate-pt-from-closed-in-metric' on page 1 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 835.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:small-ball-inside-ball' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 836.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 135 undefined on input line 837.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:d-closed-sets' on page 1 undefined on input line 8</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">37.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:disk-closed' on page 1 undefined on input line 837</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:separation-axioms' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 855.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def-item:regular' on page 135 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 855.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:separate-pt-from-closed-in-metric' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 855.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 135 undefined on input line 860.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:d-closed-sets' on page 1 undefined on input line 8</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">60.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:singleton-closed-in-metric' on page 1 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 860.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:separate-pt-from-closed-in-metric' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 860.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{corollary.26}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.864 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:separate-pts-in-metric}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:direct-proof-separate-pts-in-metric' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 870.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:separate-pts-in-metric' on page 135 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 870.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:separate-pt-from-closed-in-metric' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 870.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:separation-axioms' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 872.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def-item:T2' on page 135 undefined on input line 872.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:separate-pts-in-metric' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 875.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[135]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:dist-pt-to-set' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 893.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[136]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:open-sets-properties-in-metric-space' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 998.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:union-of-d-open-sets-is-d-open' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 998.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[137]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:separate-pts-in-metric' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 1041.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:separate-pt-from-closed-in-metric' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 1041.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sup-metric-on-functions' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 1045.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1066.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[138]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:d-closed-is-G-delta' on page 1 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 1188.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:dist-to-A-less-dist-to-B-in-open' on page 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> undefined on input line 1214.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:separate-pts-in-metric' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 1215.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[139]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:separation-axioms' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 1220.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def-item:normal' on page 140 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1220.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:pseudometric' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1259.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:separate-pts-in-metric' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 1265.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:pseudometric-identify-distance-0' on page 1 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 1270.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:ultrametric' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">284.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:p-adic-metric' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1285.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sequence-space-metric' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 1286.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/MetricSpaces/equivalent.tex [140]pdfTeX warning (ext4): destination w</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ith the same identifier (name{proposition.33}) has been already used, duplicate</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.31 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:equiv-metrics-via-balls} [141]pdfTeX warning (ext4): destinati</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on with the same identifier (name{proposition.34}) has been already used, dupli</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">cate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.68 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:d-and-dmax-equiv}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:equiv-metrics-via-balls' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 78.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:taxicab-equiv-euclidean' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 110.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sup-metric-on-functions' on page 142 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 123.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:L1-metric-on-functions' on page 142 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 123.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[142]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:dmax-vs-done' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">42.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:func-not-in-ball' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 163.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[143]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:bded-metric-equiv-to-given' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 180.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ax:R-order-complete' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 198.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[144]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:bounded' on page 1 undefined on input line 220.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{proposition.3</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">8}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.250 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:bded-metric-equiv-to-given} [145]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:bded-metric-equiv-to-given' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 292.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 146 undefined on input line 294.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:limits-in-calculus' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 294.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:limits-at-infty' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 294.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:infinite-limits' on page 146 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 294.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[146]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:map-R-to-interval' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 342.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[147] [148] [149] [150]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:translation-rotation-invariant-metrics' on page </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1 undefined on input line 571.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.43</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.582 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:isometry} [151]pdfTeX warning (ext4): destination with the sam</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e identifier (name{examples.44}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.610 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:isometries}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:translation-rotation-invariant-metrics' on page </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1 undefined on input line 635.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (25.85425pt too wide) detected at line 643</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'JacobBaileyLinearAlgebra' on page 152 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 648.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'ChrisCooperIsometries' on page 152 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 648.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'ChrisCooperIsometries3D' on page 152 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 648.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'FlemingSeveralVars2Ed' on page 152 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 648.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'KConradIsometries' on page 152 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 648.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:ip-and-isometry' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 649.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[152]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'FlemingSeveralVars2Ed' on page 153 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 701.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'KConradIsometries' on page 153 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 701.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.61795pt too wide) detected at line 746</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\OML/hlcm/m/it/10 d[]Ñy[]; y[]Ö \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 d[][]fÑx[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Ö; fÑx[]Ö[] \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 dÑx[]; x[]Ö \OMS/hlcy/m/n/10 É</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \OML/hlcm/m/it/10 d[]f[]Ñy[]Ö; f[]Ñy[]Ö[]: []</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:isometries-equiv-relation' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 753.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.46</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.765 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:top-equiv-metric-spaces} [153]pdfTeX warning (ext4): destinati</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on with the same identifier (name{examples.47}) has been already used, duplicat</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.786 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:top-equiv-metric-spaces}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:equivalent-metrics' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 793.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:equiv-metrics-implies-top-equiv' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 797.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (16.05836pt too wide) in paragraph at lines 831--832</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) The met-ric space $\OML/hlcm/m/it/10 ÑÜ\T1/hlh/m/n/10 (-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">20) 0\OML/hlcm/m/it/10 ; cá; dÖ$ \T1/hlh/m/n/10 (-20) is topo-log-i-cally equiv</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-a-lent to $\OML/hlcm/m/it/10 ÑÜa; bá; d[]Ö$\T1/hlh/m/n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[154]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (25.11824pt too wide) in paragraph at lines 843--846</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) ---the com-pos-ite of a trans-la-tion fol-lowed by a di-la</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-tion or contraction---</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:isometries-equiv-relation' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 862.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:top-equiv-metric-reflexive' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 892.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 155 undefined on input line 892.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:top-equiv-metric-spaces' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 892.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:equiv-metrics-implies-top-equiv' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 892.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:spaces' on page 1 undefined on input line 897.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[155]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:cf-taxicab-euclidean-d' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 916.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:def-metric-on-seq-bded-metric-spaces' on pa</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ge 1 undefined on input line 945.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sequence-space-metric' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 945.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:hilbert-space-and-cube' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 952.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:hilbert-cube' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 952.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 953.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:diam-ball-equal-diam-disk-Rn' on page 156 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 985.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.39265pt too wide) in paragraph at lines 993--995</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Let $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) be the col</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-lec-tion of all nonempty $\OML/hlcm/m/it/10 d$\T1/hlh/m/n/10 (-20) -closed sub</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-sets of a bounded</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[156]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:dist-between-sets' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 1005.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:translation-rotation-invariant-metrics' on page </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1 undefined on input line 1018.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1025.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1042.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[157]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:norm-properties' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1071.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:CS-inequality' on page 158 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1081.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:CS-inequality' on page 158 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1081.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:euclidean-ip' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1107.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:translation-rotation-invariant-metrics' on page </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1 undefined on input line 1119.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[158]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:top-equiv-metric-symmetric' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 1158.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:top-equiv-metric-transitive' on page 1 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 1158.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:top-equiv-metric-equiv-relation' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 1158.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/MetricSpaces/contconv.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:metrics' on page 1 undefined on input line 16.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.49</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.20 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:cont-metric} [159]pdfTeX warning (ext4): destination with the s</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ame identifier (name{examples.50}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.51 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:cont-metric}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:cont-metric' on page 1 undefined on input line 58</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1430) has occurred while \output is active [160]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[161]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:max-metric-on-product' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 163.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.56319pt too wide) in paragraph at lines 181--181</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:cont-metric' on page 1 undefined on input line 19</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">7.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:cont-metric' on page 1 undefined on input line 19</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">7.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[162]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (21.48416pt too wide) in paragraph at lines 222--223</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/it/10 (-20) For each $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/it/10 (-20) -</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">neighborhood $\OML/hlcm/m/it/10 N$ \T1/hlh/m/it/10 (-20) of $\OML/hlcm/m/it/10 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fÑxÖ$ \T1/hlh/m/it/10 (-20) in $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/it/10 (-20) ther</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e ex-ists some $\OML/hlcm/m/it/10 d$\T1/hlh/m/it/10 (-20) -neighborhood</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1 undefined on input line 234.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n page 1 undefined on input line 234.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n page 1 undefined on input line 235.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">' on page 1 undefined on input line 235.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">' on page 1 undefined on input line 236.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1 undefined on input line 236.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1 undefined on input line 241.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n page 1 undefined on input line 241.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1 undefined on input line 242.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:pf-1then2-metric-cont-at-pt' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 253.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1 undefined on input line 253.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:pf-1then2-metric-cont-at-pt' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 253.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1 undefined on input line 253.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 258.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 258.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n page 1 undefined on input line 262.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">' on page 1 undefined on input line 262.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n page 1 undefined on input line 263.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n page 1 undefined on input line 265.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[163]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:pf-2then3-metric-cont-at-pt' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 274.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 278.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 278.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">' on page 1 undefined on input line 287.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1 undefined on input line 287.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">' on page 1 undefined on input line 288.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">' on page 1 undefined on input line 291.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.13252pt too wide) in paragraph at lines 288--293</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Assume []. Let $\OML/hlcm/m/it/10 " > \T1/hlh/m/n/10 (-2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0) 0$. Since $\OML/hlcm/m/it/10 B[]ÑfÑxÖ\T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0 d[]Ö$ \T1/hlh/m/n/10 (-20) is a $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/n/10 (-20) -</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">neighborhood</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">' on page 1 undefined on input line 312.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:metric-open-map-nowhere-cont' on page 1 undefine</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">d on input line 326.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[164]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 334.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 337.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 343.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.55005pt too wide) in paragraph at lines 343--344</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) From [] we may now de-duce an es-pe-cially sim-ple cri-t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e-rion for continuity---</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:d-open-iff-nbd-each-pt' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 367.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">' on page 165 undefined on input line 369.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 370.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n page 165 undefined on input line 373.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 373.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:continuity-in-metric-via-open-sets' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 391.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[165]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:contconv' on page 1 undefined on input line 400.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:R-archimedean' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">450.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[166]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ineq:dxnx-less-than-1' on page 167 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 514.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ineq:dxnx-less-than-1' on page 167 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 514.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{examples.59})</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.527 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:seq-conv-metric} [167]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:upper-lower-bounds' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 541.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:conv-seq-bded' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 547.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.81577pt too wide) in paragraph at lines 547--548</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) In fact, in view of [], the range $\OMS/hlcy/m/n/10 f []</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> g$ \T1/hlh/m/n/10 (-20) will cer-tainly be bounded</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:increasing-seq-R-bded-above-converges' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 568.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 568.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `page-comment:sum-sqs-ell2-bded-above-converges' on pa</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ge 1 undefined on input line 568.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[168]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:conv-seq-bded' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 598.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:conv-in-whole-metric-not-in-subsp' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 606.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:rationals-order-dense-in-reals' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 626.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[169]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sup-metric-on-functions' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 667.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[170]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:seq-conv-metric' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 701.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:conv-via-nbds-metric' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 723.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[171]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:coordinatewise-conv-seq-R2' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 748.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:coordinatewise-conv-seq-Rk' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 756.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:d-and-dmax-equiv' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 791.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:conv-seq-invariant-of-equiv-metrics' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 791.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[172]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:seq-conv-Rn-iff-conv-coordinatewise' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 829.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:max-metric-on-product' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 829.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[173]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:separate-pts-in-metric' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 844.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (9.75574pt too wide) in paragraph at lines 844--847</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Just sup-pose that $\OML/hlcm/m/it/10 x \LMR/hlcm/m/n/10</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> î \OML/hlcm/m/it/10 y$\T1/hlh/m/n/10 (-20) . By [] there are dis-joint $\OML/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lcm/m/it/10 d$\T1/hlh/m/n/10 (-20) -neighborhoods</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 174 undefined on input line 862.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:seq-conv-metric' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 862.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:conv-in-whole-metric-not-in-subsp' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 862.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:unique-seq-lim-metric' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 866.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1331) has occurred while \output is active [174]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:set-d-closed' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">922.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:seq-limit-in-set' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 922.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:set-d-closed' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">923.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:seq-limit-in-set' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 928.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:set-d-closed' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">928.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:seq-limit-in-set' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 929.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:seq-limit-in-set' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 941.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[175]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 975.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 989.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cont-via-seq-conv-metric' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 1015.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[176]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:extended-reals' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1038.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:balls-at-infinity-in-extended-reals' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 1056.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 1061.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:conv-via-nbds-metric' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 1061.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[177]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:cont-metric' on page 1 undefined on input line 10</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">81.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.8464pt too wide) in paragraph at lines 1114--1116</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) of ad-di-tion and mul-ti-pli-ca-tion, re-spec-tively, are </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">$\OML/hlcm/m/it/10 Ñd[]; dÖ$\T1/hlh/m/n/10 (-20) -continuous. </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[178]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:max-metric-on-product' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 1184.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:proj-finite-prod-metric-is-cont' on page 1 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">undefined on input line 1192.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:metric-on-seq-bded-metric-spaces' on page 1 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 1192.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1207.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sequence-space-metric' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 1211.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[179]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sup-metric-on-functions' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 1226.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:L1-metric-on-functions' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1227.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:euclidean-ip' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1252.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:euclidean-ip' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1261.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `inlinedef:convex' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">280.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:inv-im-closed-is-closed-metric' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 1285.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:ip-cont-metric' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1285.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[180]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:seq-conv-metric' on page 181 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 1317.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 181 undefined on input line 1328.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:increasing-seq-R-bded-above-converges' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 1328.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:increasing-seq-R-bded-above-converges' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 1328.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[181]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:p-adic-metric' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1374.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:seq-conv-Rn-iff-conv-coordinatewise' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 1382.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sequence-space-metric' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 1382.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:seq-conv-Rn-iff-conv-coordinatewise' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 1385.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1385.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sup-metric-on-functions' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 1399.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex-part:ptwise-conv-not-sup-conv' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 1402.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:L1-metric-on-functions' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1402.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:pseudometric' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1431.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:unique-seq-lim-metric' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 1432.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/MetricSpaces/complete.tex [182]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:bounded-fn' on page 1 undefined on input line 20</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:NIP' on page 1 undefined on input line 68.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cpt-via-fip' on page 1 undefined on input line 96</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[183]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:rationals-order-dense-in-reals' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 120.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `term:category' on page 1 undefined on input line 143.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:Baire-cat-in-loc-cpt' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 143.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 184 undefined on input line 145.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:totally-disconnected' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 145.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:explosion-pt' on page 1 undefined on input line 14</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">5.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'BoasPrimerReal1996' on page 184 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 145.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Citation 'GoldbergReal1976' on page 184 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">145.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `app:close-piecewise-linear' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 149.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[184]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.25098pt too wide) in paragraph at lines 197--199</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) For ex-am-ple, any isom-e-try from $\OML/hlcm/m/it/10 ÑX; </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">dÖ$ \T1/hlh/m/n/10 (-20) and $\OML/hlcm/m/it/10 ÑY; d[]Ö$ \T1/hlh/m/n/10 (-20) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">is $\OML/hlcm/m/it/10 Ñd; d[]Ö$\T1/hlh/m/n/10 (-20) -uniformly</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) [185] (./main/TopologicalSpaces/chapterTopological.tex [186]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/topological-init.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/topologies.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:continuity-in-metric-via-open-sets' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 12.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 5954) has occurred while \output is active [187]pdfTeX</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> warning (ext4): destination with the same identifier (name{definition.2}) has </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.59 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:topological-space} [188]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:d-open' on page 1 undefined on input line 87.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:topology' on page 1 undefined on input line 87.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:open-sets-properties-in-metric-space' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 87.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:metricspace' on page 1 undefined on input line 9</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">7.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex-topology-induced-by-metric' on page 1 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 105.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:d-and-dmax-equiv' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 120.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 189 undefined on input line 135.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:d-closed-sets' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">35.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:everything-open-closed-for-discrete-d' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 135.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[189]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 190 undefined on input line 153.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:continuous-maps' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 153.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:coarser-finer-topologies' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 153.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:discrete-topology' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 155.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:indiscrete-topology' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 155.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[190]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:closed-sets-properties-in-metric-space' on page 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> undefined on input line 257.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 3118) has occurred while \output is active [191]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:closed-sets-properties-in-metric-space' on page 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> undefined on input line 288.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:closed-sets-properties-in-metric-space' on page 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> undefined on input line 289.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:open-sets-properties-in-metric-space' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 290.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:open-sets-properties-in-metric-space' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 291.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 192 undefined on input line 313.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:d-open-in-R-etc' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 313.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:open-sets-subset-metric' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 313.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[192]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:open-in-subspace' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 398.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:subspace-topology' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 418.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:subspace' on page 1 undefined on input line 418.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:rel-topology-induced-by-metric' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 420.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `convention:usual-top-on-subset-of-Rn' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 445.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[193]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:extended-reals' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">451.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:extended-reals-dhat-induces-equiv-metric-on-R' o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n page 1 undefined on input line 453.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[194]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:subspace' on page 1 undefined on input line 496.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:closed-in-subspace' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 496.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{proposition.1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.505 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> [195]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 196 undefined on input line 604.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topologies' on page 1 undefined on input line 604.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Sierpinski-space' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 604.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:included-and-excluded-pt-topologies' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 628.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:included-pt-topology' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 628.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[196]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:separation' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">693.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:separation' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">693.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[197]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:T1-space' on page 1 undefined on input line 719.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:pseudometric' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">725.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:open-etc-for-pseudometric' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 726.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 198 undefined on input line 736.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topologies' on page 1 undefined on input line 736.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Sierpinski-space' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 736.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:T1-space' on page 1 undefined on input line 740.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[198]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:T1-space' on page 1 undefined on input line 814.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:T1-space' on page 1 undefined on input line 846.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/TopologicalSpaces/neighborhoods.tex [199]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:d-nbd' on page 1 undefined on input line 36.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 200 undefined on input line 49.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topologies' on page 1 undefined on input line 49.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:finite-compl-topology' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 49.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[200]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:d-open-iff-nbd-each-pt' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 109.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{proposition.1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">5}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.112 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:open-iff-nbd-each-pt}pdfTeX warning (ext4): destination with </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">the same identifier (name{definition.16}) has been already used, duplicate igno</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">red</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.123 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:nbd-of-set} [201]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:nbd-axioms' on page 202 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">91.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:topology' on page 202 undefined on input line 206</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:nbd-axioms' on page 1 undefined on input line 207</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:topology-from-nbds' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 208.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[202]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:topology-from-nbds' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 215.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:line-with-two-origins' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 234.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:topology-from-nbds' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 241.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[203]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:topology-from-nbds' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 260.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:nbd-x-half-disk-space' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 271.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:topology-from-nbds' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 280.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[204]pdfTeX warning (ext4): destination with the same identifier (name{examples</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.21}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.322 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:hausdorff-spaces}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 205 undefined on input line 327.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topology-via-nbds' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 327.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:line-with-2-origins' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 327.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 205 undefined on input line 342.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topology-via-nbds' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 342.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:half-disk-space' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 342.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 205 undefined on input line 344.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topology-via-nbds' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 344.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:half-disk-space' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 344.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:half-disk-space-non-metrizable' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 350.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[205]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:nbds-in-subspace' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 389.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:T1-space' on page 1 undefined on input line 411.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[206]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:continuity-in-metric-via-open-sets' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 467.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:continuous' on page 1 undefined on input line 467</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:embedding' on page 1 undefined on input line 557</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:embedding' on page 1 undefined on input line 557</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:separate-pt-from-closed-in-metric' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 561.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:separate-pts-in-metric' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 561.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[207]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:T0-intro' on page 1 undefined on input line 595.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:T1-space' on page 1 undefined on input line 596.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:regular-equivalents' on page 208 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 597.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:subspace-of-regular' on page 208 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 597.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:metric-is-normal' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 598.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:distances-pts-to-sets' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 598.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cpt-T2-is-normal' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 599.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:separation' on page 1 undefined on input line 600</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 208 undefined on input line 620.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topologies' on page 1 undefined on input line 620.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Sierpinski-space' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 620.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:countable-complement-topology' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 623.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:included-and-excluded-pt-topologies' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 626.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:nbd-axioms' on page 1 undefined on input line 676</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[208]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 209 undefined on input line 712.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hausdorff-spaces' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 712.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:half-disk-space' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 712.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:topology-from-nbds' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 723.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[209]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:limit-pt' on page 1 undefined on input line 795.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 210 undefined on input line 817.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topologies' on page 1 undefined on input line 817.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Sierpinski-space' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 817.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:Fort-space-regular-not-metrizable' on page 1 und</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">efined on input line 855.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (11.06798pt too wide) in paragraph at lines 855--856</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) Note: \T1/hlh/m/n/10 (-20) A reg-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">u-lar space, even a reg-u-lar $\OML/hlcm/m/it/10 T[]$\T1/hlh/m/n/10 (-20) -spac</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e, need not be metrizable---</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/TopologicalSpaces/boundary.tex [210]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:annulus-pts' on page 1 undefined on input line 18</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[211]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:ops-and-local-base' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 71.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:bdy-relative' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">93.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subfig:pt-inside-ball' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 111.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subfig:pt-outside-disk' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 161.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[212]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:pt-on-ball-bdy' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 171.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `intuit:bdy' on page 1 undefined on input line 199.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[213]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:open-in-terms-of-bdy' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 260.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:bdy-of-complement' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 260.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:closed-in-terms-of-bdy' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 262.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:open-in-terms-of-bdy' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 262.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[214]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.27}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.283 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""> <br class="webkit-block-placeholder"></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:closure' on page 1 undefined on input line 298.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:closure' on page 1 undefined on input line 298.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:cls-int-duality' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 299.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{proposition.2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">8}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.315 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:interior-pt-via-nbds}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `txt:annular-set' on page 1 undefined on input line 35</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">7.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `txt:annular-set' on page 1 undefined on input line 35</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">7.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[215]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:rationals-order-dense-in-reals' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 367.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:interior-pt-via-nbds' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 370.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:open-iff-equals-interior' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 371.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:interior-pt-via-nbds' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 416.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:interior-pt-via-nbds' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 422.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-pf-part:open-subset-in-interior' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 422.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{corollary.31}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.430 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:open-iff-equals-interior} [216]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-part:subset-preserve-interior' on page 1 undefine</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">d on input line 474.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:interior-and-inclusion-and-intersection' on page </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1 undefined on input line 485.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-part:interior-preserve-intersection' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 485.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 217 undefined on input line 493.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:interiors' on page 1 undefined on input line 493.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:rationals-interior' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 493.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:cls-int-duality' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 522.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:bdy' on page 1 undefined on input line 531.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:interiors' on page 1 undefined on input line 531.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[217]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `intuit:bdy' on page 1 undefined on input line 577.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `intuit:int' on page 1 undefined on input line 577.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:extended-reals' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">612.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:closure-in-terms-of-nbhds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 614.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:balls-at-infinity-in-extended-reals' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 614.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:contconv' on page 1 undefined on input line 621.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[218]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:closure-in-terms-of-nbhds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 625.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:dist-pt-to-set' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 625.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:closure-in-terms-of-nbhds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 648.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:d-dense' on page 1 undefined on input line 648.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:closure-in-terms-of-nbhds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 660.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 219 undefined on input line 681.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:closure' on page 1 undefined on input line 681.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:cls-of-Q' on page 1 undefined on input line 681.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:infty-in-cls' on page 1 undefined on input line 69</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">9.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:closure-in-terms-of-nbhds' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 708.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[219]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:compl-of-int' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 776.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cls-int-duality' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 783.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cls-int-duality' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 799.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{corollary.41}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.802 F</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> or every subset $A$ of a topological space $X$:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cls-int-duality' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 832.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:cls-int-duality' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 832.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:int-largest-open' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 833.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:cls-int-duality' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 833.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-part:cls-as-int-compl' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 833.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:int-largest-open' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 833.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[220]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:int-largest-open' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 860.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:int-largest-open-means' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 860.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:cls-int-duality' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 864.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-part:cls-as-int-compl' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 864.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:closed-iff-equals-closure' on page 1 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 887.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:open-iff-equals-interior' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 887.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:cls-int-duality' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 887.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:interior-and-inclusion-and-intersection' on page </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1 undefined on input line 889.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:cls-int-duality' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 921.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-part:cls-as-int-compl' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 921.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:DeMorgans-laws' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">921.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:interior-and-inclusion-and-intersection' on page </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1 undefined on input line 921.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-part:interior-preserve-intersection' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 921.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[221]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor-part:closure-preserve-union' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 942.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.45</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.962 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:nowhere-dense}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cls-int-duality' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 973.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:compl-of-int' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 973.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:Baire-category-thm' on page 222 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 979.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[222]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.46}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.989 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:meager set}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:intersect-dense-opens' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 1033.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:meager-has-empty-int' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 1033.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:intersect-dense-opens' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 1042.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cls-int-duality' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1055.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-part:compl-of-cls' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 1055.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[223]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:meager-has-empty-int' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 1065.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:intersect-dense-opens' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 1065.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:meager-has-empty-int' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 1065.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop-part:open-is-nonmeager' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 1065.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:bdy' on page 1 undefined on input line 1074.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:bdy-line-in-plane' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 1074.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cls-smallest-closed' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 1117.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:int-largest-open' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 1125.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[224]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 225 undefined on input line 1198.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topologies' on page 1 undefined on input line 1198</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Sierpinski-space' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1198.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 225 undefined on input line 1201.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topology-via-nbds' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 1201.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:right-interval-topology-R' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 1201.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 225 undefined on input line 1204.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topology-via-nbds' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 1204.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:line-with-2-origins' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 1204.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 225 undefined on input line 1207.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hausdorff-spaces' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1207.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:half-disk-space' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1207.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:tangent-disk-space' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 1210.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[225]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:separation-axioms' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 1261.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[226]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `inlinedef:convex' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">310.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:limit-pt' on page 1 undefined on input line 1341</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/TopologicalSpaces/bases.tex [227]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:metric-local-bases' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 80.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:metric-local-bases' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 80.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[228]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:metric-local-bases' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 107.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 229 undefined on input line 107.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topologies' on page 1 undefined on input line 107.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:d-infinity-topology-on-Rn' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 107.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:d-and-dmax-equiv' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 107.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:metric-local-bases' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 111.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 229 undefined on input line 115.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topology-via-nbds' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 115.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:half-disk-space' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 115.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[229]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:2nd-countable' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">161.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:separable' on page 1 undefined on input line 161.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.53</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.165 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:1st-countable}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 230 undefined on input line 195.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topology-via-nbds' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 195.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:half-disk-space' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 195.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[230]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 231 undefined on input line 239.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:top-from-base' on page 1 undefined on input line 2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">39.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topology-ptwise-convergence-all-fns-R-to-R' on pag</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1 undefined on input line 239.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.55</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.253 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:base}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:open-union-of-base-members' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 273.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{examples.56})</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.278 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:bases}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:small-ball-inside-ball' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 296.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:d-open-iff-union-d-balls' on page 1 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 296.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:all-balls-base-of-metric' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 304.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[231]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:all-balls-base-of-metric' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 315.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 232 undefined on input line 329.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topology-via-nbds' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 329.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:line-with-2-origins' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 329.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:bases' on page 1 undefined on input line 341.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:whole-top-is-base' on page 232 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 341.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:open-cubes-base-of-Rn' on page 232 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 341.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:local-base' on page 1 undefined on input line 342.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:nbd-sys-local-base' on page 232 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 342.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:open-cubes-local-base-Rn' on page 232 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 342.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:base-of-X' on page 1 undefined on input line 375</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:local-base-at-x-in-X' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 375.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:local-base-at-x-in-X' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 382.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:base-of-X' on page 1 undefined on input line 382</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:local-base-at-x-in-X' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 392.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:base-vs-local-base' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 406.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:base-vs-local-base' on page 232 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 406.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 232 undefined on input line 407.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:1st-countable' on page 1 undefined on input line 4</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">07.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:metrizable-is-1st-countable' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 407.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[232]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:base-vs-local-base' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 441.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:base-vs-local-base' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 455.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:topology-from-nbds' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 457.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:topology-from-nbds' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 462.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:N2' on page 233 undefined on input line 463.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:N4' on page 233 undefined on input line 463.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:topology-from-nbds' on page 233 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 463.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:N1' on page 233 undefined on input line 464.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:N3' on page 233 undefined on input line 464.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B1' on page 233 undefined on input line 465.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B2' on page 233 undefined on input line 465.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:N5' on page 233 undefined on input line 466.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:topology-from-nbds' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 470.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:base-vs-local-base' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 478.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B2' on page 233 undefined on input line 487.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:base-member-open' on page 233 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 491.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:open-union-of-base-members' on page 233 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 491.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:base' on page 1 undefined on input line 492.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B1' on page 233 undefined on input line 493.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B2' on page 233 undefined on input line 493.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:top-from-base' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">494.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[233]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:base' on page 1 undefined on input line 499.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:base-member-open' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 499.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:open-union-of-base-members' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 499.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:top-from-base' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">503.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B1' on page 234 undefined on input line 503.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B1' on page 234 undefined on input line 503.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{examples.59})</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.508 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:top-from-base}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:total-ordering' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 518.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B1' on page 234 undefined on input line 529.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B2' on page 234 undefined on input line 530.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 234 undefined on input line 550.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:bases' on page 1 undefined on input line 550.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:open-ints-base-of-R' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 550.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:extended-reals' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">557.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[234]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:extended-reals' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">569.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:extended-reals-dhat-induces-equiv-metric-on-R' o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n page 1 undefined on input line 575.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:balls-at-infinity-in-extended-reals' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 601.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:balls-at-infinity-in-extended-reals' on page 1 un</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">defined on input line 615.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex-case:plus-infty' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 620.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B1' on page 235 undefined on input line 636.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:top-from-base' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">636.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B2' on page 235 undefined on input line 636.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:top-from-base' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">640.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 650.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[235]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:top-from-base' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">667.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:3-fns-thru-4-windows' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 682.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B1' on page 236 undefined on input line 700.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B2' on page 236 undefined on input line 700.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (39.92242pt too wide) in paragraph at lines 676--701</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \T1/hlh/m/n/10 (-20) De-fine $\OMS/hlcy/m/n/10 B$ \T1/hlh/m/n/10 (-20) to be t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">he col-lec-tion of all such sub-sets $\OML/hlcm/m/it/10 B[]x[]; x[]; [] ; x[] \</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[]; [] ; I[][]$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (15.45676pt too wide) in paragraph at lines 676--701</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) of $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) for all pos-s</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">i-ble choices of $\OML/hlcm/m/it/10 k$\T1/hlh/m/n/10 (-20) , of $\OML/hlcm/m/it</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/10 Ñ[]Ö$\T1/hlh/m/n/10 (-20) , and of $\OML/hlcm/m/it/10 Ñ[]Ö$\T1/hlh/m/n/10 (</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B1' on page 236 undefined on input line 702.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `property:B2' on page 236 undefined on input line 705.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:top-from-base' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">715.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:converge' on page 1 undefined on input line 718.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[236]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 5985) has occurred while \output is active [237]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 238 undefined on input line 771.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:1st-countable' on page 1 undefined on input line 7</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">71.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:metrizable-is-1st-countable' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 771.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:max-metric' on page 1 undefined on input line 805</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:d-and-dmax-equiv' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 813.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cond:local-base-at-x-in-X' on page 238 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 816.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:base-vs-local-base' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 816.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:rational-cube-inside' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 827.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[238]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:base-vs-local-base' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 870.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 2828) has occurred while \output is active [239]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 240 undefined on input line 931.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:top-from-base' on page 1 undefined on input line 9</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">31.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Sorgenfrey-line' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 931.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:in-2nd-countable-each-base-contains-countable-bas</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e' on page 1 undefined on input line 936.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (34.01646pt too wide) in paragraph at lines 935--942</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] [] []$ \T1/hlh/m/n/10 (-20) would have to con-tain some count-able base $[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] []$.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:dense-set' on page 1 undefined on input line 948.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[240]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 241 undefined on input line 969.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:dense' on page 1 undefined on input line 969.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:rationals-irrationals-dense' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 969.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 241 undefined on input line 972.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:dense' on page 1 undefined on input line 972.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:dense-subsets-of-discrete' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 972.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 241 undefined on input line 974.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:2nd-countable' on page 1 undefined on input line 9</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">74.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:2nd-countable-discrete' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 974.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 241 undefined on input line 980.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:2nd-countable' on page 1 undefined on input line 9</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">80.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Rn-is-2nd-countable' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 980.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 987.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[241]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sup-metric-on-functions' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 1031.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:compactmetric' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1035.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:compact' on page 1 undefined on input line 1035.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `app:close-piecewise-linear' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 1035.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 242 undefined on input line 1064.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:top-from-base' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">064.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:order-topology' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1064.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[242]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:no-intersect-empty-collection' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 1077.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:tangent-disk-space' on page 1 undefined on input</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> line 1090.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 243 undefined on input line 1103.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:1st-countable' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">103.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Fort-topology' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">103.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 243 undefined on input line 1151.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:1st-countable' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">151.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Fort-topology' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">151.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:compact' on page 1 undefined on input line 1194.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:cover' on page 1 undefined on input line 1194.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[243]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 244 undefined on input line 1200.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:top-from-base' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">200.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Sorgenfrey-line' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1200.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:dictionary-order' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 1208.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 244 undefined on input line 1216.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:top-from-base' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">216.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:order-topology' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1216.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 244 undefined on input line 1216.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:top-from-base' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">216.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:right-interval-topology' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 1216.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 244 undefined on input line 1236.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topologies' on page 1 undefined on input line 1236</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:finite-compl-topology' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 1236.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:countable-complement-topology' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 1239.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 244 undefined on input line 1242.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topology-via-nbds' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 1242.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:half-disk-space' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1242.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 244 undefined on input line 1246.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:top-from-base' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">246.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Sorgenfrey-line' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 1246.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:nbd-axioms' on page 1 undefined on input line 125</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">2.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) [244] (./main/ContinuityConvergence/chapterContinuityConvergence.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/continuityconvergence-init.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/continuous.tex [245]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:inequiv-metrics-on-fns' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 52.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (18.96858pt too wide) in paragraph at lines 52--53</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Example [] con-cern-ing the set $\OML/hlcm/m/it/10 X$ \T</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">1/hlh/m/n/10 (-20) of all con-tin-u-ous func-tions $\OML/hlcm/m/it/10 x [] [] Ü</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) 0\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 1\OML/hlcm/m/it/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 á [] \LMR/hlcm/m/n/10 R$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:cf-3-topologies-on-R' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 54.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (13.0625pt too wide) in paragraph at lines 56--59</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/10 S\OML/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$ \T1/hlh/m/n/10 (-2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0) is also con-tin-u-ous as a map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 T\OML/hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$\T1/hlh/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 246 undefined on input line 66.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:continuous-maps' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 66.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:coarser-finer-topologies' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 66.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/ContinuityConvergence/homeomorphism.tex [246])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/productspace.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:max-metric-on-product' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 16.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[247]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:metric-on-seq-bded-metric-spaces' on page 1 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 50.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:dprime-prod-formula' on page 248 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 65.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[248]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:graph-homeomorph-of-dom' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 116.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:graph-closed-if-continuous' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 125.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:graph-closed-if-continuous' on page 1 undef</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ined on input line 128.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 128.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/ContinuityConvergence/quotientspace.tex [249])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/convergence.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:WHAT' on page 1 undefined on input line 8.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{proposition.5</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.35 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:unif-conv-implies-ptwise-conv} [250]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:extended-reals' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">73.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) [251] (./main/Compact/chapterCompact.tex [252]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Compact/compact-init.tex) (./main/Compact/compact.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [253]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ax:R-order-complete' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 28.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[254]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:metricspace' on page 1 undefined on input line 7</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">8.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:sup-metric-on-functions' on page 1 undefined on in</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">put line 78.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:unit-interval-compact' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 113.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `eq:balls-cover-I' on page 255 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 121.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:unit-interval-compact' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 129.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[255]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:cont-interval-to-R-bded' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 137.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[256]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:unit-interval-compact' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 214.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.5}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.218 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:cpt}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:cpt' on page 1 undefined on input line 234.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `sec:compactmetric' on page 1 undefined on input line </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">235.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:sequentially-cpt' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 236.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metrizable-space-conditions-cpt' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 236.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{examples.6}) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.241 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:cpt-spaces}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:unit-interval-compact' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 249.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[257]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:finite-space-cpt' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 301.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 258 undefined on input line 320.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topologies' on page 1 undefined on input line 320.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:indiscrete-topology' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 320.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 258 undefined on input line 328.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:topologies' on page 1 undefined on input line 328.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:finite-compl-topology' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 328.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[258]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.7}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.367 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:fip} [259]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cpt-via-fip' on page 1 undefined on input line 41</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">7.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `hm:unit-interval-compact' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 457.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 260 undefined on input line 457.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:cpt-spaces' on page 1 undefined on input line 457.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:open-intervals-rays-noncpt' on page 1 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 457.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[260]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:subspace-cpt-via-cover-of-whole-space' on page 1 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">undefined on input line 482.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:open-cover-closed-subspace-of-cpt' on page 1 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 484.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[261]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:cpt-metrizable-is-totally-bded' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 541.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 544.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{example.15}) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.568 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:Cantor-K}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:closed-in-compact-is-compact' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 592.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:unit-interval-compact' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 592.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:Heine-Borel-thm' on page 262 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 592.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:Heine-Borel-thm' on page 262 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 592.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cpt-subset-of-T2-is-closed' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 606.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Command \i invalid in math mode on input line 612.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Command \i invalid in math mode on input line 612.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[262]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cpt-subset-of-T2-is-closed' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 656.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:separate-pt-from-cpt-in-T2' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 656.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:separate-disj-cpts-in-T2' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 656.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:closed-in-compact-is-compact' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 659.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:separate-disj-cpts-in-T2' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 659.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:closed-in-compact-is-compact' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 676.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[263]pdfTeX warning (ext4): destination with the same identifier (name{corollar</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">y.20}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.698 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:quotient-of-cpt-is-cpt}pdfTeX warning (ext4): destination with</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> the same identifier (name{corollary.21}) has been already used, duplicate igno</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">red</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.706 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:homeomorph-of-cpt-is-cpt}pdfTeX warning (ext4): destination wi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">th the same identifier (name{corollary.22}) has been already used, duplicate ig</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.725 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:cont-from-cpt-to-T2-is-closed}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:cont-bij-cpt-to-T2-is-homeo' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 741.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `def:dist-pt-to-set' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 775.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[264]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:extreme-value-thm' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 781.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:dist-pt-to-set-continuous' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 785.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:dist-pt-to-set-continuous' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 785.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:tube-slice-R-times-I' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 810.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[265]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `fig:cover-of-slice' on page 1 undefined on input line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 853.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[266] [267]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:tube-lemma' on page 268 undefined on input line 9</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">24.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:tube-lemma' on page 268 undefined on input line 9</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">24.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cont-image-cpt-is-cpt' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 949.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[268]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.73897pt too wide) in paragraph at lines 1010--1012</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) log-i-cal space $\OML/hlcm/m/it/10 X$ \T1/hlh/m/n/10 (-20)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> to a com-pact space $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/n/10 (-20) whose graph $[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cpt-via-nets' on page 1 undefined on input line 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">014.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (8.11954pt too wide) in paragraph at lines 1013--1015</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]$ \T1/hlh/m/n/10 (-20) con-verges to $\OML/hlcm/m/it/10 fÑxÖ$ \T1/hlh/m/n/10 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(-20) in $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/n/10 (-20) by ap-ply-ing [] to $[]$. </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/Compact/compactmetric.tex [269]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cpt-metrizable-implies-2nd-countable' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 47.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metrizable-separable-iff-2nd-countable' on page 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> undefined on input line 52.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:hilbert-space-and-cube' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 53.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob-part:hilbert-cube' on page 1 undefined on input </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">line 53.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cpt-metrizable-implies-2nd-countable' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 54.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:tychonoff-thm-denumerable-metric-case' on page 1 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">undefined on input line 64.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:cpt-subset-metric-is-bded' on page 1 undefined on</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> input line 67.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[270]pdfTeX warning (ext4): destination with the same identifier (name{proposit</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ion.36}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.103 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:cpt-metrizable-is-totally-bded}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:total-bded-criterion' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 120.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{examples.37})</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.131 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:totally-bded}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:cpt-metrizable-is-totally-bded' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 148.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:subset-of-totally-bded-is-totally-bded' on page 1 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">undefined on input line 148.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:open-interval-not-totally-bded' on page 1 undefine</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">d on input line 158.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:R-not-totally-bded' on page 1 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 158.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[271]pdfTeX warning (ext4): destination with the same identifier (name{proposit</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ion.38}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.182 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:totally-bded-is-2nd-countable}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metrizable-separable-iff-2nd-countable' on page 1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> undefined on input line 192.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:total-bded-criterion' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 194.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:totally-bded-is-2nd-countable' on page 1 undefin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed on input line 201.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cpt-via-nets' on page 1 undefined on input line 2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">46.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[272]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:metrizable-cpt' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 287.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:countably-cpt' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 287.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:sequences-cluster' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 287.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:sequentially-cpt' on page 1 undefined o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n input line 287.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:in-1st-countable-seq-clusters-if-subseq-converges</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">' on page 1 undefined on input line 287.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:countably-cpt' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 291.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:sequences-cluster' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 291.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:countably-cpt' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 293.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:sequences-cluster' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 293.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:sequences-cluster' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 303.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:countably-cpt' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 303.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:sequences-cluster' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 305.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:countably-cpt' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 305.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1168) has occurred while \output is active [273]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:countably-cpt' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 314.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:metrizable-cpt' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 314.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:countably-cpt' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 314.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:metrizable-cpt' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 314.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:cpt-metrizable-is-totally-bded' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 316.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:Lindelof' on page 274 undefined on input line 317</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:Lindelof' on page 274 undefined on input line 317</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:total-bded-criterion' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 319.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:sequences-cluster' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 331.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm-condition:countably-cpt' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 331.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 345.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:a-sequentially-cpt-fn-space-not-cpt' on page 1 u</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ndefined on input line 345.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 347.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 347.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:OmegaPlus-exists' on page 1 undefined on input li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ne 352.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[274]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metrizable-space-conditions-cpt' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 382.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:limit-pt' on page 1 undefined on input line 382.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.42</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.385 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:limit-pt}pdfTeX warning (ext4): destination with the same iden</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">tifier (name{corollary.43}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.394 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:limit-pt-in-cpt-metrizable}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metrizable-space-conditions-cpt' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 405.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metrizable-space-conditions-cpt' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 410.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:Heine-Borel-thm' on page 275 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 428.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:Heine-Borel-thm' on page 275 undefined on input l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ine 428.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[275]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metrizable-space-conditions-cpt' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 435.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:Heine-Borel-thm' on page 1 undefined on input lin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e 475.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metrizable-space-conditions-cpt' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 478.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:cpt-iff-complete-and-totally-bded' on page 1 unde</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fined on input line 481.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:metrizable-space-conditions-cpt' on page 1 undefi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ned on input line 482.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:tychonoff-finite-family' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 502.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prop:bded-metric-equiv-to-given' on page 1 undefined </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on input line 508.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[276]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `prob:unif-cont' on page 1 undefined on input line 543</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[277]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (49.65659pt too wide) in paragraph at lines 660--662</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) [\T1/hlh/m/it/10 (-20) Hint: \T1/hlh/m/n/10 (-20) Form t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">he col-lec-tion $\OMS/hlcy/m/n/10 f [] g$ \T1/hlh/m/n/10 (-20) where $\OML/hlcm</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/m/it/10 E[] \OMS/hlcy/m/n/10 É f [] g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/Compact/locallycompact.tex [278])) [279]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Connected/chapterConnected.tex [280]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Connected/connected-init.tex) (./main/Connected/connected.texpdfTeX war</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ning (ext4): destination with the same identifier (name{definition.1}) has been</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.12 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:connected} [281]pdfTeX warning (ext4): destination with the sam</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e identifier (name{lemma.4}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.71 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {lem:conn-in-open-closed-it-meets}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:disconnected-criteria' on page 1 undefined on inp</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut line 81.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/Connected/components.texpdfTeX warning (ext4): destination with the s</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ame identifier (name{definition.5}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.15 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:component} [282]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cor:conn-set-in-unique-component' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 46.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `lem:conn-in-open-closed-it-meets' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 46.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `subsec:totally-disconnected' on page 1 undefined on i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nput line 53.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:R-subspace-conn-iff-interval' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 58.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.8}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.76 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:totally-disconnected} [283]pdfTeX warning (ext4): destination w</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ith the same identifier (name{examples.9}) has been already used, duplicate ign</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.90 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:totally-disconnected}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 284 undefined on input line 98.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:components' on page 1 undefined on input line 98.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Q-components' on page 1 undefined on input line 98</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Cantor-K' on page 1 undefined on input line 107.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `chap:compact' on page 1 undefined on input line 108.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Cantor-K' on page 1 undefined on input line 108.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:R-subspace-conn-iff-interval' on page 1 undefined</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> on input line 110.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:Cantor-K' on page 1 undefined on input line 116.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[284]) (./main/Connected/pathconnected.tex) (./main/Connected/homotopy.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Connected/simplyconnected.tex [285])) [286]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Embedding/chapterEmbedding.tex (./main/Embedding/separation.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Embedding/metrization.texpdfTeX warning (ext4): destination with the sa</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">me identifier (name{proposition.1}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.12 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> pdfTeX warning (ext4): destination with the same identifier (name{namedthe</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">orem.2}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.30 ...theorem}[name=Urysohn Metrization Theorem]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> [287])) [288])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./back/backmatter.tex (./back/exerciseguide.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 23--23</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 23--25</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 27--27</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 27--29</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 31--31</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 31--33</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 35--35</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 35--37</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 39--39</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 39--41</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 42--42</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 42--44</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 46--46</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 46--48</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 50--50</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 50--52</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 54--54</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 54--56</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 58--58</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 58--60</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 62--62</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 62--64</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 66--66</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 66--68</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 70--70</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 70--72</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 74--74</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 74--76</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 78--78</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 78--80</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[289] [290]) (./back/indexes.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file topologybook.nls.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file notation.gls.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file names.ind.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file topologybook.ind.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) (./topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file front/frontmatter.aux.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file front/preface.aux.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/chapterSetsMaps.aux) (./main/MetricSpaces/chapterMetrics.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/chapterTopological.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/chapterContinuityConvergence.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Compact/chapterCompact.aux) (./main/Connected/chapterConnected.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Embedding/chapterEmbedding.aux) (./back/backmatter.aux))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Dependency list written on topologybook.dep.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package rerunfilecheck Warning: File `topologybook.out' has changed.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(rerunfilecheck) Rerun to get outlines right</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(rerunfilecheck) or use package `bookmark'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: There were undefined references.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Please (re)run BibTeX on the file(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) topologybook</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) and rerun LaTeX afterwards.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> )</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(see the transcript file for additional information){/usr/local/texlive/2017/te</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">xmf-dist/fonts/enc/dvips/base/8r.enc}</Users/murray/Library/texmf/fonts/type1/b</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">h/lucida/lbd.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbdi.pfb></</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Users/murray/Library/texmf/fonts/type1/bh/lucida/lbi.pfb></Users/murray/Library</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/texmf/fonts/type1/bh/lucida/lbma.pfb></Users/murray/Library/texmf/fonts/type1/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">bh/lucida/lbme.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbmo.pfb></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbmr.pfb></Users/murray/Libr</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ary/texmf/fonts/type1/bh/lucida/lbms.pfb></Users/murray/Library/texmf/fonts/typ</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e1/bh/lucida/lbmsd.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbr.p</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lsd.pfb></Users/murray/Li</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">brary/texmf/fonts/type1/bh/lucida/lsdi.pfb></Users/murray/Library/texmf/fonts/t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ype1/bh/lucida/lsi.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lsr.p</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fb></usr/local/texlive/2017/texmf-dist/fonts/type1/public/xypic/xyatip10.pfb></</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">usr/local/texlive/2017/texmf-dist/fonts/type1/public/xypic/xybtip10.pfb></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Output written on topologybook.pdf (294 pages, 1069203 bytes).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">SyncTeX written on topologybook.synctex.gz.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Transcript written on topologybook.log.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'notation.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'names.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'topologybook.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Non-existent bbl file 'topologybook.bbl'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> No file topologybook.bbl.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'topologybook.nls' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file topologybook.nls.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'topologybook.nls' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file topologybook.nls.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'notation.gls' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file notation.gls.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'notation.gls' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file notation.gls.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'names.ind' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file names.ind.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'names.ind' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file names.ind.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'topologybook.ind' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file topologybook.ind.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'topologybook.ind' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file topologybook.ind.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Log file says output to 'topologybook.pdf'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Couldn't find aux file 'front/frontmatter.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Couldn't find aux file 'front/preface.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">=== TeX engine is 'pdfTeX'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Found bibliography file(s) [mytopologybook.bib mytopologyread.bib topologybook-blx.bib]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Summary of warnings:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Latex failed to resolve 1135 reference(s)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Latex failed to resolve 19 citation(s)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'cusdep nlo nls topologybook': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.nlo'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Non-existent destination files:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.nls'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 1 of rule 'cusdep nlo nls topologybook'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">=== Creating rule for 'cusdep nlo nls topologybook'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'cusdep nlo nls topologybook'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">For rule 'cusdep nlo nls topologybook', running '&do_cusdep( makenlo2nls )' ...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning style file /usr/local/texlive/2017/texmf-dist/makeindex/nomencl/nomencl.ist..........done (10 attributes redefined, 3 ignored).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning input file topologybook.nlo....done (140 entries accepted, 0 rejected).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sorting entries....done (990 comparisons).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Generating output file topologybook.nls....done (293 lines written, 0 warnings).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Output written in topologybook.nls.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Transcript written in topologybook.ilg.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'makeindex topologybook.idx': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.idx'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Non-existent destination files:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.ind'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 1 of rule 'makeindex topologybook.idx'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'makeindex -s "topologybook".ist -o "topologybook.ind" "topologybook.idx"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'makeindex topologybook.idx'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning style file ./topologybook.ist......done (6 attributes redefined, 0 ignored).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning input file topologybook.idx.....done (1105 entries accepted, 3 rejected).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sorting entries...........done (11822 comparisons).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Generating output file topologybook.ind.....done (949 lines written, 147 warnings).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Output written in topologybook.ind.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Transcript written in topologybook.ilg.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'bibtex topologybook': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Non-existent destination files:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.bbl'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 1 of rule 'bibtex topologybook'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'bibtex "topologybook"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'bibtex topologybook'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">For rule 'bibtex topologybook', running '&run_bibtex( )' ...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is BibTeX, Version 0.99d (TeX Live 2017)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">The top-level auxiliary file: topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">The style file: biblatex.bst</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I couldn't open auxiliary file front/frontmatter.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">---line 25 of file topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : \@input{front/frontmatter.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : }</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I'm skipping whatever remains of this command</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I couldn't open auxiliary file front/preface.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">---line 39 of file topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : \@input{front/preface.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : }</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I'm skipping whatever remains of this command</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/SetsMaps/chapterSetsMaps.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/MetricSpaces/chapterMetrics.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/TopologicalSpaces/chapterTopological.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/ContinuityConvergence/chapterContinuityConvergence.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/Compact/chapterCompact.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/Connected/chapterConnected.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/Embedding/chapterEmbedding.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: back/backmatter.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Database file #1: topologybook-blx.bib</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Database file #2: mytopologybook.bib</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Database file #3: mytopologyread.bib</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Biblatex version: 3.3</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(There were 2 error messages)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: One or more aux files is missing for bibtex. I'll try</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> to get (pdf)latex to remake them.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'makeindex notation.idx': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'notation.idx'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Non-existent destination files:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'notation.ind'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 1 of rule 'makeindex notation.idx'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'makeindex -s "topologybook".ist -o "notation.ind" "notation.idx"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'makeindex notation.idx'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning style file ./topologybook.ist......done (6 attributes redefined, 0 ignored).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning input file notation.idx...done (0 entries accepted, 0 rejected).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Nothing written in notation.ind.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Transcript written in notation.ilg.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'makeindex names.idx': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'names.idx'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Non-existent destination files:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'names.ind'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 1 of rule 'makeindex names.idx'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'makeindex -s "topologybook".ist -o "names.ind" "names.idx"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'makeindex names.idx'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning style file ./topologybook.ist......done (6 attributes redefined, 0 ignored).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning input file names.idx....done (44 entries accepted, 0 rejected).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sorting entries....done (249 comparisons).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Generating output file names.ind....done (100 lines written, 0 warnings).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Output written in names.ind.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Transcript written in names.ilg.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'pdflatex': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'TopologyEd2metadata.xmpi'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'back/backmatter.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Compact/chapterCompact.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Connected/chapterConnected.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/ContinuityConvergence/chapterContinuityConvergence.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Embedding/chapterEmbedding.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/MetricSpaces/chapterMetrics.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/SetsMaps/chapterSetsMaps.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/TopologicalSpaces/chapterTopological.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'names.ind'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'notation.ind'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.bbl'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.ind'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.nls'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.out'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 2 of rule 'pdflatex'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'pdflatex --synctex=1 --file-line-error -recorder "topologybook.tex"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'pdflatex'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017) (preloaded format=pdflatex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> restricted \write18 enabled.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">entering extended mode</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX2e <2017-04-15></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Babel <3.12> and hyphenation patterns for 84 language(s) loaded.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/snapshot/snapshot.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/memoir.cls</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Document Class: memoir 2016/05/16 v3.7f configurable book, report, article docu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ment class</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ifpdf.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/ifetex/ifetex.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/plain/ifetex/ifetex.tex))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/ifxetex/ifxetex.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ifluatex.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/mem10.clo)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/mempatch.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/base/ifthen.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./preamble/preamble.tex (./preamble/packages.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/csquotes/csquotes.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/etoolbox/etoolbox.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/graphics/keyval.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/csquotes/csquotes.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/csquotes/csquotes.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/amsmath/amsmath.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">For additional information on amsmath, use the `?' option.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/amsmath/amstext.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/amsmath/amsgen.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/amsmath/amsbsy.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/amsmath/amsopn.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/amscls/amsthm.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/l3packages/xfrac/xfrac.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/l3kernel/expl3.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/l3kernel/expl3-code.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/l3kernel/l3pdfmode.def))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/graphics/graphicx.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/graphics/graphics.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/graphics/trig.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/graphics-cfg/graphics.cfg)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/graphics-def/pdftex.def)))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/l3packages/l3keys2e/l3keys2e.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> (/usr/local/texlive/2017/texmf-dist/tex/latex/base/textcomp.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/base/ts1enc.def))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/l3packages/xparse/xparse.sty)</div><div style="margin: 0px; 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xstring/xstring.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xstring/xstring.tex))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/xpatch/xpatch.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/bigfoot/suffix.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/xcolor/xcolor.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/graphics-cfg/color.cfg)</div><div style="margin: 0px; font-size: 11px; 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/base/t1enc.def))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucimatx/lucimatx.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/tools/bm.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/my/mymath.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/mathtools/mathtools.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/mathtools/mhsetup.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/centernot.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/scalerel/scalerel.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/my/mywidebar.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/my/myaccents.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Using mymath variant defs for Lucida Bright.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Using mymath variant defs for Lucida Bright.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (/Users/murray/Library/texmf/tex/generic/diagxy/diagxy.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xy.tex Bootstrap'ing:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">catcodes, docmode,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyrecat.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyidioms.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic version 3.8.9 <2013/10/06></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Copyright (c) 1991-2013 by Kristoffer H. Rose <<a href="mailto:krisrose@tug.org" class="">krisrose@tug.org</a>> and others</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic is free software: see the User's Guide for details.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Loading kernel: messages; fonts; allocations: state, direction,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">utility macros; pictures: \xy, positions, objects, decorations;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">kernel objects: directionals, circles, text; options; algorithms: directions,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">edges, connections; Xy-pic loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyarrow.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic option: Arrow and Path feature v.3.9 path, \ar, loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xycurve.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic option: Curve and Spline extension v.3.12 curve, circles, loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucida/t1hlh.fd))) (./preamble/style.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">******************************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Stock height and width: 794.96999pt by 614.295pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Top and edge trims: 0pt and 0pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Page height and width: 663pt by 456pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Text height and width: 538pt by 336pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Spine and edge margins: 60pt and 60pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Upper and lower margins: 67.5pt and 57.5pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Headheight and headsep: 12pt and 18.06749pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Footskip: 25.29494pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Columnsep and columnseprule: 10pt and 0pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Marginparsep and marginparwidth: 7pt and 46pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidecapsep and sidecapwidth: 7pt and 128pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidebarhsep and sidebarwidth: 7pt and 128pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidebarvsep and sidebartopsep: 12pt and 0pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidebarheight: 548.39996pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidefoothsep and sidefootwidth: 7pt and 128pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidefootvsep and sidefootheight: 12pt and 548.39996pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">******************************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucida/t1hls.fd))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./preamble/mathdefs.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/mathtools/empheq.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thmtools.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-patch.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/parseargs.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-kv.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/infwarerr.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/etexcmds.sty)))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-autoref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/aliasctr.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/carlisle/remreset.sty)))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-listof.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-restate.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-amsthm.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">****************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Made patch specific for amsthm.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">****************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./preamble/links.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/biblatex.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ltxcmds.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/kvoptions.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/logreq/logreq.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/logreq/logreq.def))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/url/url.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/blx-dm.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/blx-compat.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/blx-bibtex.def</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Using fall-back BibTeX(8) backend:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) functionality may be reduced/unavailable.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/biblatex.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/biblatex/bbx/mybooknumeric.bbx</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/bbx/standard.bbx)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/bbx/numeric.bbx))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/cbx/numeric.cbx)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./biblatex.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/nomencl/nomencl.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Using the configuration file nomencl.cfg</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./nomencl.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/repeatindex/repeatindex.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/tools/afterpage.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/hyperref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/auxhook.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/pd1enc.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/latexconfig/hyperref.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/memhfixc.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Message: Driver (autodetected): hpdftex.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/hpdftex.def</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Option `pdftex' has already been used,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) setting the option has no effect on input line 107.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/xmpincl/xmpincl.sty)<<TopologyEd2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">metadata.xmpi>></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperxmp/hyperxmp.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/stringenc.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/doclicense/doclicense.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/xifthen/xifthen.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/tools/xspace.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/doclicense/doclicense-english.ldf</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) (/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/aliascnt.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/cleveref/cleveref.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./preamble/labels.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/showlabels/showlabels.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package: `showlabels' v1.8 <2016/06/09></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">with amsmath equation tags</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">))) (/usr/local/texlive/2017/texmf-dist/tex/latex/microtype/microtype.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/microtype/microtype-pdftex.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/microtype/microtype.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing nomenclature file topologybook.nlo</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing index file notation.idx </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing index file names.idx </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing index file topologybook.idx </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/biblatex/lbx/mylanguagestrings.lbx</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/lbx/english.lbx))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/ccicons/ccicons.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/xkeyval/xkeyval.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xkeyval/xkeyval.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xkeyval/xkvutils.tex))))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file front/frontmatter.aux.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file front/preface.aux.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/chapterSetsMaps.aux) (./main/MetricSpaces/chapterMetrics.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/chapterTopological.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/chapterContinuityConvergence.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Compact/chapterCompact.aux) (./main/Connected/chapterConnected.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Embedding/chapterEmbedding.aux) (./back/backmatter.aux))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/base/ts1cmr.fd)</div><div style="margin: 0px; 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">ABD: EveryShipout initializing macros (./topologybook.bbl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Biber reported the following issues</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) with 'Bernays1991':</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) - Can't use 'location' + 'address'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; 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font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Biber reported the following issues</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) with 'GaillardZorn2017':</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) - Invalid format of field 'urldate'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Biber reported the following issues</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) with 'GraysonZorn2007':</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) - Invalid format of field 'urldate'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/nameref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/gettitlestring.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Redoing nameref's sectioning</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Redoing nameref's label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.out) (./topologybook.out)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/se-pdfdoc.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/se-utf8.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.toc [1{/Users/murray/Library/texlive/2017/texmf-var/fonts/map/p</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">dftex/updmap/pdftex.map}]) [2] (./topologybook.toc [3] [4] [5]) [6]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/mainmatter.tex (./main/SetsMaps/chapterSetsMaps.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/setsmaps-init.tex) (./main/SetsMaps/logic.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [1])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/sets.tex [2] [3] [4] [5] [6]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucidabr/omshlh.fd) [7] [8] [9] [10]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[11] [12]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (38.67267pt too wide) in paragraph at lines 733--734</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) verse re-la-tion $[]$ is \T1/hlh/m/it/10 (-20) not \T1/hlh</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/m/n/10 (-20) func-tional be-cause the set $\OMS/hlcy/m/n/10 f [] g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[13] [14]) (./main/SetsMaps/maps.tex [15] [16] [17] [18] [19] [20] [21]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[22] [23] [24] [25] [26] [27] [28]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.20296pt too wide) in paragraph at lines 934--935</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) In examples ([][]*[][]) of the subsection ``Injections, </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">surjections, and bijections''</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[29] [30] [31]) (./main/SetsMaps/families.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 48.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 48.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[32]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 116.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 116.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[33] [34] [35] [36]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.7854pt too wide) in paragraph at lines 368--369</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) The union and in-ter-sec-tion of two sets in the sense o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">f sub-sec-tion ``Union</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.96655pt too wide) in paragraph at lines 372--374</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) Moreover, the for-mu-las in-volv-ing union and in-ter-sec-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">tion in sub-sec-tion ``Union</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[37] [38] [39] [40] [41] [42] [43] [44]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.57535pt too wide) in paragraph at lines 909--910</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Let $\OML/hlcm/m/it/10 n$ \T1/hlh/m/n/10 (-20) be a pos-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">i-tive in-te-ger and let $\OML/hlcm/m/it/10 ÑX[]Ö[]$ \T1/hlh/m/n/10 (-20) be a </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fam-ily of \T1/hlh/m/it/10 (-20) nonempty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[45]) (./main/SetsMaps/recursion.tex [46] [47] [48] [49] [50] [51] [52])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/countable.tex [53]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.3389pt too wide) in paragraph at lines 84--88</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) Hence the map ob-tained from $\OML/hlcm/m/it/10 h[]$ \T1/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lh/m/n/10 (-20) by re-strict-ing its do-main to $\OMS/hlcy/m/n/10 f\T1/hlh/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ; n;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> n \OMS/hlcy/m/n/10 Ç</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[54]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.72176pt too wide) in paragraph at lines 152--155</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Now let $\OML/hlcm/m/it/10 n \OMS/hlcy/m/n/10 ^^U \T1/hl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">h/m/n/10 (-20) 1$ and as-sume that each sub-set of $\OMS/hlcy/m/n/10 f\T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> n\OMS/hlcy/m/n/10 g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[55] [56] [57] [58] [59] [60] [61] [62] [63]) (./main/SetsMaps/ordering.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[79]) (./main/SetsMaps/ordercomplete.tex [80] [81] [82] [83])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/equivrel.tex [84]) (./main/SetsMaps/well-ordering.tex [85]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[86] [87] [88]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 300.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[89] [90] [91] [92]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 619.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[93]</div><div style="margin: 0px; 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[98] [99] [100] [101] [102]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `superscript' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[103]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.6}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.384 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:taxicab-metric} [104] [105]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucida/ts1hlh.fd) [106] [107]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (9.80023pt too wide) in paragraph at lines 624--625</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hls/b/n/10 1.9 Ex-am-ple. []\T1/hlh/m/n/10 (-20) Again let $\OML/hlcm/m/i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t/10 X$ \T1/hlh/m/n/10 (-20) be the set of all con-tin-u-ous func-tions $\OML/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lcm/m/it/10 x [] [] Ü\T1/hlh/m/n/10 (-20) 0\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-20) 1\OML/hlcm/m/it/10 á [] \LMR/hlcm/m/n/10 R$\T1/hlh/m/n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[108] [109] [110] [111] [112] [113] [114]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.90543pt too wide) in paragraph at lines 1092--1093</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Are the taxi-cab and max met-rics on $\LMR/hlcm/m/n/10 R</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]$ \T1/hlh/m/n/10 (-20) also translation-invariant?</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[115] [116] [117] [118]) (./main/MetricSpaces/openclosed.tex [119] [120]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[121] [122] [123] [124] [125] [126] [127] [128] [129] [130]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 2846) has occurred while \output is active [131]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[132] [133] [134]pdfTeX warning (ext4): destination with the same identifier (n</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ame{corollary.26}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.864 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:separate-pts-in-metric} [135] [136] [137] [138] [139] [140])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/MetricSpaces/equivalent.texpdfTeX warning (ext4): destination with the </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">same identifier (name{proposition.33}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.31 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:equiv-metrics-via-balls} [141]pdfTeX warning (ext4): destinati</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on with the same identifier (name{proposition.34}) has been already used, dupli</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">cate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.68 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:d-and-dmax-equiv} [142]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1454) has occurred while \output is active [143]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[144]pdfTeX warning (ext4): destination with the same identifier (name{proposit</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ion.38}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.250 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:bded-metric-equiv-to-given} [145] [146] [147] [148] [149]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[150]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.43}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.582 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:isometry} [151]pdfTeX warning (ext4): destination with the sam</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e identifier (name{examples.44}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.610 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:isometries}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (25.85425pt too wide) detected at line 643</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[152]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.61795pt too wide) detected at line 746</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\OML/hlcm/m/it/10 d[]Ñy[]; y[]Ö \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 d[][]fÑx[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Ö; fÑx[]Ö[] \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 dÑx[]; x[]Ö \OMS/hlcy/m/n/10 É</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \OML/hlcm/m/it/10 d[]f[]Ñy[]Ö; f[]Ñy[]Ö[]: []</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[153]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.46}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.765 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:top-equiv-metric-spaces}pdfTeX warning (ext4): destination wit</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">h the same identifier (name{examples.47}) has been already used, duplicate igno</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">red</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.786 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:top-equiv-metric-spaces} [154]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (16.05836pt too wide) in paragraph at lines 831--832</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) The met-ric space $\OML/hlcm/m/it/10 ÑÜ\T1/hlh/m/n/10 (-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">20) 0\OML/hlcm/m/it/10 ; cá; dÖ$ \T1/hlh/m/n/10 (-20) is topo-log-i-cally equiv</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-a-lent to $\OML/hlcm/m/it/10 ÑÜa; bá; d[]Ö$\T1/hlh/m/n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (25.11824pt too wide) in paragraph at lines 843--846</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) ---the com-pos-ite of a trans-la-tion fol-lowed by a di-la</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-tion or contraction---</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[155] [156]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.39265pt too wide) in paragraph at lines 993--995</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Let $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) be the col</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-lec-tion of all nonempty $\OML/hlcm/m/it/10 d$\T1/hlh/m/n/10 (-20) -closed sub</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-sets of a bounded</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[157] [158]) (./main/MetricSpaces/contconv.texpdfTeX warning (ext4): destinatio</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n with the same identifier (name{definition.49}) has been already used, duplica</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">te ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.20 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:cont-metric} [159]pdfTeX warning (ext4): destination with the s</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ame identifier (name{examples.50}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.51 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:cont-metric} [160] [161]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.56319pt too wide) in paragraph at lines 181--181</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[162]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (21.48416pt too wide) in paragraph at lines 222--223</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/it/10 (-20) For each $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/it/10 (-20) -</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">neighborhood $\OML/hlcm/m/it/10 N$ \T1/hlh/m/it/10 (-20) of $\OML/hlcm/m/it/10 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fÑxÖ$ \T1/hlh/m/it/10 (-20) in $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/it/10 (-20) ther</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e ex-ists some $\OML/hlcm/m/it/10 d$\T1/hlh/m/it/10 (-20) -neighborhood</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[163]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (8.2688pt too wide) in paragraph at lines 288--293</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Assume ([][]3[][]). Let $\OML/hlcm/m/it/10 " > \T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) 0$. Since $\OML/hlcm/m/it/10 B[]ÑfÑxÖ\T1/hlh/m/n/10 (-20) ; \OML/hl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">cm/m/it/10 d[]Ö$ \T1/hlh/m/n/10 (-20) is a $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/n/1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0 (-20) -neighborhood</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[164] [165] [166] [167]pdfTeX warning (ext4): destination with the same identif</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ier (name{examples.59}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.527 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:seq-conv-metric} [168] [169] [170] [171] [172]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1097) has occurred while \output is active [173]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[174] [175] [176] [177]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.8464pt too wide) in paragraph at lines 1114--1116</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) of ad-di-tion and mul-ti-pli-ca-tion, re-spec-tively, are </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">$\OML/hlcm/m/it/10 Ñd[]; dÖ$\T1/hlh/m/n/10 (-20) -continuous. </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[178] [179] [180] [181] [182]) (./main/MetricSpaces/complete.tex [183] [184]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[185]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.25098pt too wide) in paragraph at lines 197--199</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) For ex-am-ple, any isom-e-try from $\OML/hlcm/m/it/10 ÑX; </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">dÖ$ \T1/hlh/m/n/10 (-20) and $\OML/hlcm/m/it/10 ÑY; d[]Ö$ \T1/hlh/m/n/10 (-20) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">is $\OML/hlcm/m/it/10 Ñd; d[]Ö$\T1/hlh/m/n/10 (-20) -uniformly</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) [186] (./main/TopologicalSpaces/chapterTopological.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/topological-init.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/topologies.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 5954) has occurred while \output is active [187]pdfTeX</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> warning (ext4): destination with the same identifier (name{definition.2}) has </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.59 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:topological-space} [188] [189] [190] [191] [192] [193] [194]pdf</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">TeX warning (ext4): destination with the same identifier (name{proposition.11})</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.505 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> [195] [196] [197] [198]) (./main/TopologicalSpaces/neighborhoods.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[199] [200]pdfTeX warning (ext4): destination with the same identifier (name{pr</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">oposition.15}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.112 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:open-iff-nbd-each-pt}pdfTeX warning (ext4): destination with </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">the same identifier (name{definition.16}) has been already used, duplicate igno</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">red</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.123 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:nbd-of-set} [201] [202] [203] [204]pdfTeX warning (ext4): dest</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ination with the same identifier (name{examples.21}) has been already used, dup</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">licate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.322 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:hausdorff-spaces} [205] [206] [207] [208] [209]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (11.06798pt too wide) in paragraph at lines 855--856</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) Note: \T1/hlh/m/n/10 (-20) A reg-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">u-lar space, even a reg-u-lar $\OML/hlcm/m/it/10 T[]$\T1/hlh/m/n/10 (-20) -spac</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e, need not be metrizable---</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[210]) (./main/TopologicalSpaces/boundary.tex [211] [212] [213] [214]pdfTeX war</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ning (ext4): destination with the same identifier (name{definition.27}) has bee</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.283 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> pdfTeX warning (ext4): destination with the same identifier (name{proposi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">tion.28}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.315 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:interior-pt-via-nbds} [215] [216]pdfTeX warning (ext4): desti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nation with the same identifier (name{corollary.31}) has been already used, dup</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">licate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.430 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:open-iff-equals-interior} [217] [218] [219] [220]pdfTeX warnin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">g (ext4): destination with the same identifier (name{corollary.41}) has been al</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ready used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.802 F</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> or every subset $A$ of a topological space $X$: [221] [222]pdfTeX warnin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">g (ext4): destination with the same identifier (name{definition.45}) has been a</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lready used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.962 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:nowhere-dense}pdfTeX warning (ext4): destination with the same</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> identifier (name{definition.46}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.989 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:meager set} [223] [224] [225]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 226 undefined on input line 1201.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:right-interval-topology-R' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 1201.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[226] [227]) (./main/TopologicalSpaces/bases.tex [228] [229]pdfTeX warning (ext</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">4): destination with the same identifier (name{definition.53}) has been already</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.165 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:1st-countable} [230] [231]pdfTeX warning (ext4): destination w</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ith the same identifier (name{definition.55}) has been already used, duplicate </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.253 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:base}pdfTeX warning (ext4): destination with the same identifi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">er (name{examples.56}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.278 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:bases} [232] [233] [234]pdfTeX warning (ext4): destination with</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> the same identifier (name{examples.59}) has been already used, duplicate ignor</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.508 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:top-from-base} [235]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 650.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[236]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (15.12009pt too wide) in paragraph at lines 676--701</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) de-picts three mem-bers of a set of the form $\OML/hlcm/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">it/10 B[]x[]; x[]; x[]; x[] \T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[];</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> I[]; I[][]$\T1/hlh/m/n/10 (-20) .]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (39.92242pt too wide) in paragraph at lines 676--701</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \T1/hlh/m/n/10 (-20) De-fine $\OMS/hlcy/m/n/10 B$ \T1/hlh/m/n/10 (-20) to be t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">he col-lec-tion of all such sub-sets $\OML/hlcm/m/it/10 B[]x[]; x[]; [] ; x[] \</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[]; [] ; I[][]$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (15.45676pt too wide) in paragraph at lines 676--701</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) of $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) for all pos-s</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">i-ble choices of $\OML/hlcm/m/it/10 k$\T1/hlh/m/n/10 (-20) , of $\OML/hlcm/m/it</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/10 Ñ[]Ö$\T1/hlh/m/n/10 (-20) , and of $\OML/hlcm/m/it/10 Ñ[]Ö$\T1/hlh/m/n/10 (</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[237]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 5985) has occurred while \output is active [238]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[239]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 2828) has occurred while \output is active [240]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[241]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1448) has occurred while \output is active [242]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[243] [244] [245])) [246]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/chapterContinuityConvergence.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/continuityconvergence-init.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/continuous.tex [247]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (13.0625pt too wide) in paragraph at lines 56--59</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/10 S\OML/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$ \T1/hlh/m/n/10 (-2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0) is also con-tin-u-ous as a map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 T\OML/hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$\T1/hlh/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/ContinuityConvergence/homeomorphism.tex [248])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/productspace.tex [249] [250]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 128.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/ContinuityConvergence/quotientspace.tex [251])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/convergence.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:WHAT' on page 1 undefined on input line 8.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{proposition.5</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.35 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:unif-conv-implies-ptwise-conv} [252])) [253]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Compact/chapterCompact.tex [254] (./main/Compact/compact-init.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Compact/compact.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [255]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[256] [257] [258]pdfTeX warning (ext4): destination with the same identifier (n</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ame{definition.5}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.218 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:cpt}pdfTeX warning (ext4): destination with the same identifie</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">r (name{examples.6}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.241 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:cpt-spaces} [259] [260]pdfTeX warning (ext4): destination with </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">the same identifier (name{definition.7}) has been already used, duplicate ignor</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.367 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:fip} [261]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `hm:unit-interval-compact' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 457.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[262] [263]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 544.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{example.15}) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.568 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:Cantor-K} [264]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Command \i invalid in math mode on input line 612.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Command \i invalid in math mode on input line 612.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[265]pdfTeX warning (ext4): destination with the same identifier (name{corollar</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">y.20}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.698 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:quotient-of-cpt-is-cpt}pdfTeX warning (ext4): destination with</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> the same identifier (name{corollary.21}) has been already used, duplicate igno</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">red</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.706 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:homeomorph-of-cpt-is-cpt}pdfTeX warning (ext4): destination wi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">th the same identifier (name{corollary.22}) has been already used, duplicate ig</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.725 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:cont-from-cpt-to-T2-is-closed} [266] [267] [268] [269]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[270]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.73897pt too wide) in paragraph at lines 1010--1012</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) log-i-cal space $\OML/hlcm/m/it/10 X$ \T1/hlh/m/n/10 (-20)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> to a com-pact space $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/n/10 (-20) whose graph $[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[271]) (./main/Compact/compactmetric.tex [272]pdfTeX warning (ext4): destinatio</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n with the same identifier (name{proposition.36}) has been already used, duplic</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.103 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:cpt-metrizable-is-totally-bded}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [273]pdfTe</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">X warning (ext4): destination with the same identifier (name{examples.37}) has </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.131 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:totally-bded}pdfTeX warning (ext4): destination with the same i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">dentifier (name{proposition.38}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.182 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:totally-bded-is-2nd-countable} [274] [275] [276]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 345.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 347.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 347.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.42</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.385 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:limit-pt}pdfTeX warning (ext4): destination with the same iden</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">tifier (name{corollary.43}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.394 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:limit-pt-in-cpt-metrizable} [277] [278] [279] [280]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (49.65659pt too wide) in paragraph at lines 660--662</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) [\T1/hlh/m/it/10 (-20) Hint: \T1/hlh/m/n/10 (-20) Form t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">he col-lec-tion $\OMS/hlcy/m/n/10 f [] g$ \T1/hlh/m/n/10 (-20) where $\OML/hlcm</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/m/it/10 E[] \OMS/hlcy/m/n/10 É f [] g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/Compact/locallycompact.tex)) [281]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Connected/chapterConnected.tex [282]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Connected/connected-init.tex) (./main/Connected/connected.texpdfTeX war</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ning (ext4): destination with the same identifier (name{definition.1}) has been</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.12 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:connected} [283]pdfTeX warning (ext4): destination with the sam</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e identifier (name{lemma.4}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.71 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {lem:conn-in-open-closed-it-meets}) (./main/Connected/components.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.5}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.15 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:component} [284]pdfTeX warning (ext4): destination with the sam</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e identifier (name{definition.8}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.76 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:totally-disconnected} [285]pdfTeX warning (ext4): destination w</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ith the same identifier (name{examples.9}) has been already used, duplicate ign</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.90 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:totally-disconnected} [286]) (./main/Connected/pathconnected.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/Connected/homotopy.tex) (./main/Connected/simplyconnected.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[287])) [288] (./main/Embedding/chapterEmbedding.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Embedding/separation.tex) (./main/Embedding/metrization.texpdfTeX warni</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ng (ext4): destination with the same identifier (name{proposition.1}) has been </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.12 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> pdfTeX warning (ext4): destination with the same identifier (name{namedthe</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">orem.2}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.30 ...theorem}[name=Urysohn Metrization Theorem]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> [289])) [290])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./back/backmatter.tex (./back/exerciseguide.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 23--23</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 23--25</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 27--27</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 27--29</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 31--31</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 31--33</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 35--35</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 35--37</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 39--39</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 39--41</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 42--42</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 42--44</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 46--46</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 46--48</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 50--50</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 50--52</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 54--54</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 54--56</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 58--58</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 58--60</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 62--62</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 62--64</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 66--66</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 66--68</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 70--70</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 70--72</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 74--74</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 74--76</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 78--78</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 78--80</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[291] [292]) (./back/indexes.tex (./topologybook.nls [293]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [294]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[295])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file notation.gls.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[296] (./names.ind [297] [298]) (./topologybook.ind</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.76491pt too wide) in paragraph at lines 21--23</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Baire Cat-e-gory The-o-rem, [][]184[][], [][]222[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.53792pt too wide) in paragraph at lines 34--35</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Bolzano-Weierstrass The-o-rem, [][]276[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.18558pt too wide) in paragraph at lines 35--37</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) bound (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20) b</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ounded; lower bound;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[299]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.28082pt too wide) in paragraph at lines 95--97</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) co-finite topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">m/n/10 (-20) finite-com-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (11.63974pt too wide) in paragraph at lines 124--126</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) space; order-completeness) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[300]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (4.49474pt too wide) in paragraph at lines 145--146</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) and con-ver-gent se-quence, [][]176[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.13008pt too wide) in paragraph at lines 148--149</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) from Eu-clidean $\OML/hlcm/m/it/10 n$\T1/hlh/m/n/10 (-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">20) -space to real</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.131pt too wide) in paragraph at lines 149--150</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) on com-pact met-ric space, [][]277[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.44911pt too wide) in paragraph at lines 190--192</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/it/10 (-20) See also \T1/hlh/m/n/10 (-20) con-nected space; sep-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (17.60744pt too wide) in paragraph at lines 190--192</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) a-ra-tion; to-tally dis-con-nected</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.79329pt too wide) in paragraph at lines 215--216</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) distance-preserving map, [][]151[][], [][]152[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[301]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.5973pt too wide) in paragraph at lines 245--247</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Euclidean in-ner prod-uct, [][]158[][], [][]180[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.04117pt too wide) in paragraph at lines 269--270</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) extreme (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> max-i-mum,minimum) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.8835pt too wide) in paragraph at lines 282--284</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) first-category set (\T1/hlh/m/it/10 (-20) see \T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) mea-ger set) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[302]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.30344pt too wide) in paragraph at lines 323--325</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) Borel-Lebesgue The-o-rem) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.56528pt too wide) in paragraph at lines 325--326</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Heine-Borel-Lebesgue The-o-rem, [][]262[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (18.59972pt too wide) in paragraph at lines 349--350</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) see also \T1/hlh/m/n/10 (-20) e</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l-e-ment,member,subset) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.43198pt too wide) in paragraph at lines 362--364</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) tion,mathematical in-duc-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[303]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.584pt too wide) in paragraph at lines 393--394</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) of a collection of sets, [][]\T1/hlh/b/it/10 39[][]\T1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/hlh/m/n/10 (-20) , [][]39[][]--</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.77872pt too wide) in paragraph at lines 469--470</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) defined piecewise, [][]21[][]--[][]22[][], [][]38[][]-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[304]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.09427pt too wide) in paragraph at lines 495--497</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) ex-am-ples of, [][]99[][], [][]103[][]--[][]114[][], [</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">][]116[][],</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.06433pt too wide) in paragraph at lines 514--516</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) topo-log-i-cally equiv-a-lent, [][]\T1/hlh/b/it/10 154</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[][]\T1/hlh/m/n/10 (-20) ,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (8.51826pt too wide) in paragraph at lines 516--517</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) metrically equiv-a-lent met-ric spaces,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.98947pt too wide) in paragraph at lines 543--545</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) neighborhood, [][]\T1/hlh/b/it/10 200[][]\T1/hlh/m/n/10 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(-20) , [][]200[][]--[][]202[][], [][]228[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.06833pt too wide) in paragraph at lines 554--556</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Niemytzki plane (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 (-20) tan-gent disk</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[305]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (9.05663pt too wide) in paragraph at lines 573--574</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) in second-countable space, [][]272[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.59937pt too wide) in paragraph at lines 591--592</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) and mul-ti-plica-tive in-verse, [][]20[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (4.04407pt too wide) in paragraph at lines 599--601</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) order topol-ogy, [][]\T1/hlh/b/it/10 234[][]\T1/hlh/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 (-20) , [][]234[][]--[][]235[][], [][]244[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.82869pt too wide) in paragraph at lines 608--610</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) der-ing; pre-order-ing; strict</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (20.25978pt too wide) in paragraph at lines 608--610</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) weak or-der-ing; well-ordering) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[306]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.26106pt too wide) in paragraph at lines 727--729</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) func-tional re-la-tion, or-der</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[307]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.88599pt too wide) in paragraph at lines 750--752</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) second-category set (\T1/hlh/m/it/10 (-20) see \T1/hlh/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">m/n/10 (-20) non-mea-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.03703pt too wide) in paragraph at lines 752--753</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) second-countable space, [][]\T1/hlh/b/it/10 238[][]\T1/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lh/m/n/10 (-20) , [][]238[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.32431pt too wide) in paragraph at lines 768--769</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) sequential com-pact-ness, [][]273[][], [][]274[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.40741pt too wide) in paragraph at lines 775--777</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) smaller topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n/10 (-20) coarser topol-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.25479pt too wide) in paragraph at lines 781--783</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) space (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20) t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">opo-log-i-cal space, met-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.31657pt too wide) in paragraph at lines 785--786</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) statement (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0) pred-i-cate,sentence) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.04988pt too wide) in paragraph at lines 786--788</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) strict or-der-ing (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n/10 (-20) strict di-rected</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.03561pt too wide) in paragraph at lines 786--788</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) or-der-ing; strict par-tial or-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.09906pt too wide) in paragraph at lines 790--792</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) stronger topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) finer topol-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[308]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (21.70116pt too wide) in paragraph at lines 848--850</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) topologically equiv-a-lent met-ric spaces,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.37872pt too wide) in paragraph at lines 860--861</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) gen-er-ated by a col-lec-tion, [][]233[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.37599pt too wide) in paragraph at lines 871--872</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) totally bounded met-ric space, [][]\T1/hlh/b/it/10 270[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.131pt too wide) in paragraph at lines 900--901</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) on com-pact met-ric space, [][]277[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[309]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.584pt too wide) in paragraph at lines 906--907</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) of a collection of sets, [][]\T1/hlh/b/it/10 39[][]\T1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/hlh/m/n/10 (-20) , [][]39[][]--</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (8.61229pt too wide) in paragraph at lines 933--935</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) weaker topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/10 (-20) coarser topol-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[310]))) (./topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file front/frontmatter.aux.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file front/preface.aux.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/chapterSetsMaps.aux) (./main/MetricSpaces/chapterMetrics.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/chapterTopological.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/chapterContinuityConvergence.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Compact/chapterCompact.aux) (./main/Connected/chapterConnected.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Embedding/chapterEmbedding.aux) (./back/backmatter.aux))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Dependency list written on topologybook.dep.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package rerunfilecheck Warning: File `topologybook.out' has changed.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(rerunfilecheck) Rerun to get outlines right</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(rerunfilecheck) or use package `bookmark'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: There were undefined references.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Please rerun LaTeX.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) Page breaks have changed.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> )</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(see the transcript file for additional information)pdfTeX warning (dest): name</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">{cite.0@GoldbergReal1976} has been referenced but does not exist, replaced by a</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@BoasPrimerReal1996} has been referenced but </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">does not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@KConradIsometries} has been referenced but d</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">oes not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@FlemingSeveralVars2Ed} has been referenced b</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut does not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@ChrisCooperIsometries3D} has been referenced</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> but does not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@ChrisCooperIsometries} has been referenced b</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ut does not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@JacobBaileyLinearAlgebra} has been reference</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">d but does not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@GaillardZorn2017} has been referenced but do</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">es not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@GraysonZorn2007} has been referenced but doe</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">s not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@KneserZorn1950} has been referenced but does</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@Suppes1972} has been referenced but does not</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@Bernays1991} has been referenced but does no</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@EisenbergSets1971} has been referenced but d</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">oes not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@BourbakiSets2004} has been referenced but do</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">es not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@PinterSets2014} has been referenced but does</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@LakinsMathReasoning2016} has been referenced</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> but does not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@EisenbergMathMethod1996} has been referenced</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> but does not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">{/usr/local/texlive/2017/texmf-dist/fonts/enc/dvips/base/8r.enc}</Users/murray/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Library/texmf/fonts/type1/bh/lucida/lbd.pfb></Users/murray/Library/texmf/fonts/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">type1/bh/lucida/lbdi.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbma.pfb></Users/murray</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/Library/texmf/fonts/type1/bh/lucida/lbme.pfb></Users/murray/Library/texmf/font</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">s/type1/bh/lucida/lbmo.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">bmr.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbms.pfb></Users/mur</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ray/Library/texmf/fonts/type1/bh/lucida/lbmsd.pfb></Users/murray/Library/texmf/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fonts/type1/bh/lucida/lbr.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucid</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">a/lsd.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lsdi.pfb></Users/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">urray/Library/texmf/fonts/type1/bh/lucida/lsi.pfb></Users/murray/Library/texmf/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fonts/type1/bh/lucida/lsr.pfb></usr/local/texlive/2017/texmf-dist/fonts/type1/p</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ublic/xypic/xyatip10.pfb></usr/local/texlive/2017/texmf-dist/fonts/type1/public</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/xypic/xybtip10.pfb></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Output written on topologybook.pdf (316 pages, 1207459 bytes).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">SyncTeX written on topologybook.synctex.gz.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Transcript written on topologybook.log.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'notation.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'names.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'topologybook.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'notation.gls' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file notation.gls.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'notation.gls' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file notation.gls.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Log file says output to 'topologybook.pdf'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Couldn't find aux file 'front/frontmatter.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Couldn't find aux file 'front/preface.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">=== TeX engine is 'pdfTeX'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Found bibliography file(s) [mytopologybook.bib mytopologyread.bib topologybook-blx.bib]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Summary of warnings:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Latex failed to resolve 9 reference(s)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'cusdep nlo nls topologybook': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.nlo'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 2 of rule 'cusdep nlo nls topologybook'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'cusdep nlo nls topologybook'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">For rule 'cusdep nlo nls topologybook', running '&do_cusdep( makenlo2nls )' ...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning style file /usr/local/texlive/2017/texmf-dist/makeindex/nomencl/nomencl.ist..........done (10 attributes redefined, 3 ignored).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning input file topologybook.nlo....done (140 entries accepted, 0 rejected).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sorting entries....done (990 comparisons).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Generating output file topologybook.nls....done (293 lines written, 0 warnings).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Output written in topologybook.nls.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Transcript written in topologybook.ilg.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'makeindex topologybook.idx': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.idx'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 2 of rule 'makeindex topologybook.idx'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'makeindex -s "topologybook".ist -o "topologybook.ind" "topologybook.idx"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'makeindex topologybook.idx'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning style file ./topologybook.ist......done (6 attributes redefined, 0 ignored).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning input file topologybook.idx.....done (1105 entries accepted, 3 rejected).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sorting entries...........done (11818 comparisons).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Generating output file topologybook.ind.....done (951 lines written, 145 warnings).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Output written in topologybook.ind.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Transcript written in topologybook.ilg.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'bibtex topologybook': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'back/backmatter.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Compact/chapterCompact.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Connected/chapterConnected.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/ContinuityConvergence/chapterContinuityConvergence.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Embedding/chapterEmbedding.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/MetricSpaces/chapterMetrics.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/SetsMaps/chapterSetsMaps.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/TopologicalSpaces/chapterTopological.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 2 of rule 'bibtex topologybook'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'bibtex "topologybook"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'bibtex topologybook'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">For rule 'bibtex topologybook', running '&run_bibtex( )' ...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is BibTeX, Version 0.99d (TeX Live 2017)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">The top-level auxiliary file: topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">The style file: biblatex.bst</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I couldn't open auxiliary file front/frontmatter.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">---line 25 of file topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : \@input{front/frontmatter.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : }</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I'm skipping whatever remains of this command</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I couldn't open auxiliary file front/preface.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">---line 39 of file topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : \@input{front/preface.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : }</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I'm skipping whatever remains of this command</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/SetsMaps/chapterSetsMaps.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/MetricSpaces/chapterMetrics.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/TopologicalSpaces/chapterTopological.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/ContinuityConvergence/chapterContinuityConvergence.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/Compact/chapterCompact.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/Connected/chapterConnected.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/Embedding/chapterEmbedding.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: back/backmatter.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Database file #1: topologybook-blx.bib</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Database file #2: mytopologybook.bib</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Database file #3: mytopologyread.bib</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Biblatex version: 3.3</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(There were 2 error messages)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: One or more aux files is missing for bibtex. I'll try</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> to get (pdf)latex to remake them.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'makeindex names.idx': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'names.idx'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 2 of rule 'makeindex names.idx'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'makeindex -s "topologybook".ist -o "names.ind" "names.idx"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'makeindex names.idx'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning style file ./topologybook.ist......done (6 attributes redefined, 0 ignored).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Scanning input file names.idx....done (44 entries accepted, 0 rejected).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sorting entries....done (249 comparisons).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Generating output file names.ind....done (100 lines written, 0 warnings).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Output written in names.ind.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Transcript written in names.ilg.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'pdflatex': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'back/backmatter.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Compact/chapterCompact.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Connected/chapterConnected.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/ContinuityConvergence/chapterContinuityConvergence.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Embedding/chapterEmbedding.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/MetricSpaces/chapterMetrics.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/SetsMaps/chapterSetsMaps.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/TopologicalSpaces/chapterTopological.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'names.ind'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.ind'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.nls'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.out'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.run.xml'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.toc'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 3 of rule 'pdflatex'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'pdflatex --synctex=1 --file-line-error -recorder "topologybook.tex"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'pdflatex'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017) (preloaded format=pdflatex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> restricted \write18 enabled.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">entering extended mode</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX2e <2017-04-15></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Babel <3.12> and hyphenation patterns for 84 language(s) loaded.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/snapshot/snapshot.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/memoir.cls</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Document Class: memoir 2016/05/16 v3.7f configurable book, report, article docu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ment class</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ifpdf.sty)</div><div style="margin: 0px; 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font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/mathtools/mathtools.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/mathtools/mhsetup.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/centernot.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/scalerel/scalerel.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/my/mywidebar.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/my/myaccents.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Using mymath variant defs for Lucida Bright.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Using mymath variant defs for Lucida Bright.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (/Users/murray/Library/texmf/tex/generic/diagxy/diagxy.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xy.tex Bootstrap'ing:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">catcodes, docmode,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyrecat.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyidioms.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic version 3.8.9 <2013/10/06></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Copyright (c) 1991-2013 by Kristoffer H. Rose <<a href="mailto:krisrose@tug.org" class="">krisrose@tug.org</a>> and others</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic is free software: see the User's Guide for details.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Loading kernel: messages; fonts; allocations: state, direction,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">utility macros; pictures: \xy, positions, objects, decorations;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">kernel objects: directionals, circles, text; options; algorithms: directions,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">edges, connections; Xy-pic loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyarrow.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic option: Arrow and Path feature v.3.9 path, \ar, loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xycurve.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic option: Curve and Spline extension v.3.12 curve, circles, loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucida/t1hlh.fd))) (./preamble/style.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-autoref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/aliasctr.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/carlisle/remreset.sty)))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-listof.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-restate.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-amsthm.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">****************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Made patch specific for amsthm.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">****************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./preamble/links.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/biblatex.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ltxcmds.sty))</div><div style="margin: 0px; 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) (/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/aliascnt.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/cleveref/cleveref.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./preamble/labels.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/showlabels/showlabels.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package: `showlabels' v1.8 <2016/06/09></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">with amsmath equation tags</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">))) (/usr/local/texlive/2017/texmf-dist/tex/latex/microtype/microtype.sty</div><div style="margin: 0px; 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line-height: normal; font-family: Monaco;" class="">(biblatex) - Invalid format of field 'urldate'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Biber reported the following issues</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) with 'ChrisCooperIsometries3D':</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) - Invalid format of field 'urldate'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Biber reported the following issues</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) with 'GaillardZorn2017':</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) - Invalid format of field 'urldate'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Biber reported the following issues</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) with 'GraysonZorn2007':</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) - Invalid format of field 'urldate'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/nameref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/gettitlestring.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Redoing nameref's sectioning</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Redoing nameref's label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.out) (./topologybook.out)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/se-pdfdoc.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/se-utf8.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.toc [1{/Users/murray/Library/texlive/2017/texmf-var/fonts/map/p</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">dftex/updmap/pdftex.map}]) [2] (./topologybook.toc [3] [4] [5]) [6]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/mainmatter.tex (./main/SetsMaps/chapterSetsMaps.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/setsmaps-init.tex) (./main/SetsMaps/logic.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [1])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/sets.tex [2] [3] [4] [5] [6]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucidabr/omshlh.fd) [7] [8] [9] [10]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[11] [12]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (38.67267pt too wide) in paragraph at lines 733--734</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) verse re-la-tion $[]$ is \T1/hlh/m/it/10 (-20) not \T1/hlh</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/m/n/10 (-20) func-tional be-cause the set $\OMS/hlcy/m/n/10 f [] g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[13] [14]) (./main/SetsMaps/maps.tex [15] [16] [17] [18] [19] [20] [21]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[22] [23] [24] [25] [26] [27] [28]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.20296pt too wide) in paragraph at lines 934--935</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) In examples ([][]*[][]) of the subsection ``Injections, </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">surjections, and bijections''</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[29] [30] [31]) (./main/SetsMaps/families.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 48.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 48.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[32]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 116.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 116.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[33] [34] [35] [36]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.7854pt too wide) in paragraph at lines 368--369</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) The union and in-ter-sec-tion of two sets in the sense o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">f sub-sec-tion ``Union</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.96655pt too wide) in paragraph at lines 372--374</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) Moreover, the for-mu-las in-volv-ing union and in-ter-sec-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">tion in sub-sec-tion ``Union</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[37] [38] [39] [40] [41] [42] [43] [44]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.57535pt too wide) in paragraph at lines 909--910</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Let $\OML/hlcm/m/it/10 n$ \T1/hlh/m/n/10 (-20) be a pos-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">i-tive in-te-ger and let $\OML/hlcm/m/it/10 ÑX[]Ö[]$ \T1/hlh/m/n/10 (-20) be a </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fam-ily of \T1/hlh/m/it/10 (-20) nonempty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[45]) (./main/SetsMaps/recursion.tex [46] [47] [48] [49] [50] [51] [52])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/countable.tex [53]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.3389pt too wide) in paragraph at lines 84--88</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) Hence the map ob-tained from $\OML/hlcm/m/it/10 h[]$ \T1/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lh/m/n/10 (-20) by re-strict-ing its do-main to $\OMS/hlcy/m/n/10 f\T1/hlh/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ; n;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> n \OMS/hlcy/m/n/10 Ç</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[54]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.72176pt too wide) in paragraph at lines 152--155</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Now let $\OML/hlcm/m/it/10 n \OMS/hlcy/m/n/10 ^^U \T1/hl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">h/m/n/10 (-20) 1$ and as-sume that each sub-set of $\OMS/hlcy/m/n/10 f\T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> n\OMS/hlcy/m/n/10 g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[55] [56] [57] [58] [59] [60] [61] [62] [63]) (./main/SetsMaps/ordering.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[79]) (./main/SetsMaps/ordercomplete.tex [80] [81] [82] [83])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/equivrel.tex [84]) (./main/SetsMaps/well-ordering.tex [85]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[86] [87] [88]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 300.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[89] [90] [91] [92]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 619.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[93]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.15701pt too wide) in paragraph at lines 727--728</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) The pre-ced-ing proof is a typ-i-cal pro-ce-dure for ap-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ply-ing Zorn's Lemma.To</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[94] [95])) [96] (./main/MetricSpaces/chapterMetrics.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/MetricSpaces/metrics-init.tex) (./main/MetricSpaces/metrics.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[97]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.58485pt too wide) in paragraph at lines 79--79</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[98] [99] [100] [101] [102]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `superscript' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[103]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.6}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.384 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:taxicab-metric} [104] [105]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucida/ts1hlh.fd) [106] [107]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (9.80023pt too wide) in paragraph at lines 624--625</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hls/b/n/10 1.9 Ex-am-ple. []\T1/hlh/m/n/10 (-20) Again let $\OML/hlcm/m/i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t/10 X$ \T1/hlh/m/n/10 (-20) be the set of all con-tin-u-ous func-tions $\OML/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lcm/m/it/10 x [] [] Ü\T1/hlh/m/n/10 (-20) 0\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-20) 1\OML/hlcm/m/it/10 á [] \LMR/hlcm/m/n/10 R$\T1/hlh/m/n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[108] [109] [110] [111] [112] [113] [114]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.90543pt too wide) in paragraph at lines 1092--1093</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Are the taxi-cab and max met-rics on $\LMR/hlcm/m/n/10 R</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]$ \T1/hlh/m/n/10 (-20) also translation-invariant?</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[115] [116] [117] [118]) (./main/MetricSpaces/openclosed.tex [119] [120]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[121] [122] [123] [124] [125] [126] [127] [128] [129] [130]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 2846) has occurred while \output is active [131]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[132] [133] [134]pdfTeX warning (ext4): destination with the same identifier (n</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ame{corollary.26}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.864 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:separate-pts-in-metric} [135] [136] [137] [138] [139] [140])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/MetricSpaces/equivalent.texpdfTeX warning (ext4): destination with the </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">same identifier (name{proposition.33}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.31 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:equiv-metrics-via-balls} [141]pdfTeX warning (ext4): destinati</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on with the same identifier (name{proposition.34}) has been already used, dupli</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">cate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.68 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:d-and-dmax-equiv} [142]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1454) has occurred while \output is active [143]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[144]pdfTeX warning (ext4): destination with the same identifier (name{proposit</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ion.38}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.250 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:bded-metric-equiv-to-given} [145] [146] [147] [148] [149]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[150]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.43}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.582 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:isometry} [151]pdfTeX warning (ext4): destination with the sam</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e identifier (name{examples.44}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.610 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:isometries}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (25.85425pt too wide) detected at line 643</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[152]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.61795pt too wide) detected at line 746</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\OML/hlcm/m/it/10 d[]Ñy[]; y[]Ö \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 d[][]fÑx[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Ö; fÑx[]Ö[] \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 dÑx[]; x[]Ö \OMS/hlcy/m/n/10 É</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \OML/hlcm/m/it/10 d[]f[]Ñy[]Ö; f[]Ñy[]Ö[]: []</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[153]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.46}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.765 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:top-equiv-metric-spaces}pdfTeX warning (ext4): destination wit</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">h the same identifier (name{examples.47}) has been already used, duplicate igno</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">red</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.786 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:top-equiv-metric-spaces} [154]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (16.05836pt too wide) in paragraph at lines 831--832</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) The met-ric space $\OML/hlcm/m/it/10 ÑÜ\T1/hlh/m/n/10 (-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">20) 0\OML/hlcm/m/it/10 ; cá; dÖ$ \T1/hlh/m/n/10 (-20) is topo-log-i-cally equiv</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-a-lent to $\OML/hlcm/m/it/10 ÑÜa; bá; d[]Ö$\T1/hlh/m/n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (25.11824pt too wide) in paragraph at lines 843--846</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) ---the com-pos-ite of a trans-la-tion fol-lowed by a di-la</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-tion or contraction---</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[155] [156]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.39265pt too wide) in paragraph at lines 993--995</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Let $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) be the col</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-lec-tion of all nonempty $\OML/hlcm/m/it/10 d$\T1/hlh/m/n/10 (-20) -closed sub</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-sets of a bounded</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[157] [158]) (./main/MetricSpaces/contconv.texpdfTeX warning (ext4): destinatio</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n with the same identifier (name{definition.49}) has been already used, duplica</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">te ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.20 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:cont-metric} [159]pdfTeX warning (ext4): destination with the s</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ame identifier (name{examples.50}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.51 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:cont-metric} [160] [161]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.56319pt too wide) in paragraph at lines 181--181</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[162]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (21.48416pt too wide) in paragraph at lines 222--223</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/it/10 (-20) For each $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/it/10 (-20) -</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">neighborhood $\OML/hlcm/m/it/10 N$ \T1/hlh/m/it/10 (-20) of $\OML/hlcm/m/it/10 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fÑxÖ$ \T1/hlh/m/it/10 (-20) in $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/it/10 (-20) ther</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e ex-ists some $\OML/hlcm/m/it/10 d$\T1/hlh/m/it/10 (-20) -neighborhood</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[163]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (8.2688pt too wide) in paragraph at lines 288--293</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Assume ([][]3[][]). Let $\OML/hlcm/m/it/10 " > \T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) 0$. Since $\OML/hlcm/m/it/10 B[]ÑfÑxÖ\T1/hlh/m/n/10 (-20) ; \OML/hl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">cm/m/it/10 d[]Ö$ \T1/hlh/m/n/10 (-20) is a $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/n/1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0 (-20) -neighborhood</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[164] [165] [166] [167]pdfTeX warning (ext4): destination with the same identif</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ier (name{examples.59}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.527 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:seq-conv-metric} [168] [169] [170] [171] [172]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1097) has occurred while \output is active [173]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[174] [175] [176] [177]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.8464pt too wide) in paragraph at lines 1114--1116</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) of ad-di-tion and mul-ti-pli-ca-tion, re-spec-tively, are </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">$\OML/hlcm/m/it/10 Ñd[]; dÖ$\T1/hlh/m/n/10 (-20) -continuous. </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[178] [179] [180] [181] [182]) (./main/MetricSpaces/complete.tex [183] [184]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[185]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.25098pt too wide) in paragraph at lines 197--199</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) For ex-am-ple, any isom-e-try from $\OML/hlcm/m/it/10 ÑX; </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">dÖ$ \T1/hlh/m/n/10 (-20) and $\OML/hlcm/m/it/10 ÑY; d[]Ö$ \T1/hlh/m/n/10 (-20) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">is $\OML/hlcm/m/it/10 Ñd; d[]Ö$\T1/hlh/m/n/10 (-20) -uniformly</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) [186] (./main/TopologicalSpaces/chapterTopological.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/topological-init.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/topologies.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 5954) has occurred while \output is active [187]pdfTeX</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> warning (ext4): destination with the same identifier (name{definition.2}) has </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.59 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:topological-space} [188] [189] [190] [191] [192] [193] [194]pdf</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">TeX warning (ext4): destination with the same identifier (name{proposition.11})</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.505 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> [195] [196] [197] [198]) (./main/TopologicalSpaces/neighborhoods.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[199] [200]pdfTeX warning (ext4): destination with the same identifier (name{pr</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">oposition.15}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.112 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:open-iff-nbd-each-pt}pdfTeX warning (ext4): destination with </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">the same identifier (name{definition.16}) has been already used, duplicate igno</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">red</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.123 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:nbd-of-set} [201] [202] [203] [204]pdfTeX warning (ext4): dest</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ination with the same identifier (name{examples.21}) has been already used, dup</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">licate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.322 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:hausdorff-spaces} [205] [206] [207] [208] [209]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (11.06798pt too wide) in paragraph at lines 855--856</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) Note: \T1/hlh/m/n/10 (-20) A reg-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">u-lar space, even a reg-u-lar $\OML/hlcm/m/it/10 T[]$\T1/hlh/m/n/10 (-20) -spac</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e, need not be metrizable---</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[210]) (./main/TopologicalSpaces/boundary.tex [211] [212] [213] [214]pdfTeX war</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ning (ext4): destination with the same identifier (name{definition.27}) has bee</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.283 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> pdfTeX warning (ext4): destination with the same identifier (name{proposi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">tion.28}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.315 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:interior-pt-via-nbds} [215] [216]pdfTeX warning (ext4): desti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nation with the same identifier (name{corollary.31}) has been already used, dup</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">licate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.430 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:open-iff-equals-interior} [217] [218] [219] [220]pdfTeX warnin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">g (ext4): destination with the same identifier (name{corollary.41}) has been al</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ready used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.802 F</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> or every subset $A$ of a topological space $X$: [221] [222]pdfTeX warnin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">g (ext4): destination with the same identifier (name{definition.45}) has been a</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lready used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.962 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:nowhere-dense}pdfTeX warning (ext4): destination with the same</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> identifier (name{definition.46}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.989 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:meager set} [223] [224] [225]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 226 undefined on input line 1201.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:right-interval-topology-R' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 1201.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[226] [227]) (./main/TopologicalSpaces/bases.tex [228] [229]pdfTeX warning (ext</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">4): destination with the same identifier (name{definition.53}) has been already</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.165 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:1st-countable} [230] [231]pdfTeX warning (ext4): destination w</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ith the same identifier (name{definition.55}) has been already used, duplicate </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.253 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:base}pdfTeX warning (ext4): destination with the same identifi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">er (name{examples.56}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.278 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:bases} [232] [233] [234]pdfTeX warning (ext4): destination with</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> the same identifier (name{examples.59}) has been already used, duplicate ignor</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.508 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:top-from-base} [235]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 650.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[236]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (15.12009pt too wide) in paragraph at lines 676--701</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) de-picts three mem-bers of a set of the form $\OML/hlcm/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">it/10 B[]x[]; x[]; x[]; x[] \T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[];</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> I[]; I[][]$\T1/hlh/m/n/10 (-20) .]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (39.92242pt too wide) in paragraph at lines 676--701</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \T1/hlh/m/n/10 (-20) De-fine $\OMS/hlcy/m/n/10 B$ \T1/hlh/m/n/10 (-20) to be t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">he col-lec-tion of all such sub-sets $\OML/hlcm/m/it/10 B[]x[]; x[]; [] ; x[] \</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[]; [] ; I[][]$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (15.45676pt too wide) in paragraph at lines 676--701</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) of $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) for all pos-s</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">i-ble choices of $\OML/hlcm/m/it/10 k$\T1/hlh/m/n/10 (-20) , of $\OML/hlcm/m/it</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/10 Ñ[]Ö$\T1/hlh/m/n/10 (-20) , and of $\OML/hlcm/m/it/10 Ñ[]Ö$\T1/hlh/m/n/10 (</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[237]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 5985) has occurred while \output is active [238]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[239]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 2828) has occurred while \output is active [240]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[241]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1448) has occurred while \output is active [242]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[243] [244] [245])) [246]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/chapterContinuityConvergence.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/continuityconvergence-init.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/continuous.tex [247]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (13.0625pt too wide) in paragraph at lines 56--59</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/10 S\OML/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$ \T1/hlh/m/n/10 (-2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0) is also con-tin-u-ous as a map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 T\OML/hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$\T1/hlh/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/ContinuityConvergence/homeomorphism.tex [248])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/productspace.tex [249] [250]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 128.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/ContinuityConvergence/quotientspace.tex [251])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/convergence.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:WHAT' on page 1 undefined on input line 8.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{proposition.5</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.35 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:unif-conv-implies-ptwise-conv} [252])) [253]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Compact/chapterCompact.tex [254] (./main/Compact/compact-init.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Compact/compact.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [255]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[256] [257] [258]pdfTeX warning (ext4): destination with the same identifier (n</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ame{definition.5}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.218 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:cpt}pdfTeX warning (ext4): destination with the same identifie</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">r (name{examples.6}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.241 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:cpt-spaces} [259] [260]pdfTeX warning (ext4): destination with </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">the same identifier (name{definition.7}) has been already used, duplicate ignor</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.367 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:fip} [261]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `hm:unit-interval-compact' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 457.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[262] [263]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 544.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{example.15}) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.568 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:Cantor-K} [264]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Command \i invalid in math mode on input line 612.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Command \i invalid in math mode on input line 612.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[265]pdfTeX warning (ext4): destination with the same identifier (name{corollar</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">y.20}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.698 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:quotient-of-cpt-is-cpt}pdfTeX warning (ext4): destination with</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> the same identifier (name{corollary.21}) has been already used, duplicate igno</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">red</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.706 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:homeomorph-of-cpt-is-cpt}pdfTeX warning (ext4): destination wi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">th the same identifier (name{corollary.22}) has been already used, duplicate ig</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.725 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:cont-from-cpt-to-T2-is-closed} [266] [267] [268] [269]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[270]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.73897pt too wide) in paragraph at lines 1010--1012</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) log-i-cal space $\OML/hlcm/m/it/10 X$ \T1/hlh/m/n/10 (-20)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> to a com-pact space $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/n/10 (-20) whose graph $[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[271]) (./main/Compact/compactmetric.tex [272]pdfTeX warning (ext4): destinatio</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n with the same identifier (name{proposition.36}) has been already used, duplic</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.103 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:cpt-metrizable-is-totally-bded}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [273]pdfTe</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">X warning (ext4): destination with the same identifier (name{examples.37}) has </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.131 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:totally-bded}pdfTeX warning (ext4): destination with the same i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">dentifier (name{proposition.38}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.182 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:totally-bded-is-2nd-countable} [274] [275] [276]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 345.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 347.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 347.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.42</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.385 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:limit-pt}pdfTeX warning (ext4): destination with the same iden</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">tifier (name{corollary.43}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.394 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:limit-pt-in-cpt-metrizable} [277] [278] [279] [280]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (49.65659pt too wide) in paragraph at lines 660--662</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) [\T1/hlh/m/it/10 (-20) Hint: \T1/hlh/m/n/10 (-20) Form t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">he col-lec-tion $\OMS/hlcy/m/n/10 f [] g$ \T1/hlh/m/n/10 (-20) where $\OML/hlcm</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/m/it/10 E[] \OMS/hlcy/m/n/10 É f [] g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/Compact/locallycompact.tex)) [281]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Connected/chapterConnected.tex [282]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Connected/connected-init.tex) (./main/Connected/connected.texpdfTeX war</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ning (ext4): destination with the same identifier (name{definition.1}) has been</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.12 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:connected} [283]pdfTeX warning (ext4): destination with the sam</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e identifier (name{lemma.4}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.71 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {lem:conn-in-open-closed-it-meets}) (./main/Connected/components.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.5}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.15 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:component} [284]pdfTeX warning (ext4): destination with the sam</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e identifier (name{definition.8}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.76 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:totally-disconnected} [285]pdfTeX warning (ext4): destination w</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ith the same identifier (name{examples.9}) has been already used, duplicate ign</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.90 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:totally-disconnected} [286]) (./main/Connected/pathconnected.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/Connected/homotopy.tex) (./main/Connected/simplyconnected.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[287])) [288] (./main/Embedding/chapterEmbedding.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Embedding/separation.tex) (./main/Embedding/metrization.texpdfTeX warni</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ng (ext4): destination with the same identifier (name{proposition.1}) has been </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.12 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> pdfTeX warning (ext4): destination with the same identifier (name{namedthe</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">orem.2}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.30 ...theorem}[name=Urysohn Metrization Theorem]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> [289])) [290])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./back/backmatter.tex (./back/exerciseguide.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 23--23</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 23--25</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 27--27</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 27--29</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 31--31</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 31--33</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 35--35</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 35--37</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 39--39</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 39--41</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 42--42</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 42--44</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 46--46</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 46--48</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 50--50</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 50--52</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 54--54</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 54--56</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 58--58</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 58--60</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 62--62</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 62--64</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 66--66</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 66--68</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 70--70</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 70--72</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 74--74</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 74--76</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 78--78</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 78--80</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[291] [292]) (./back/indexes.tex (./topologybook.nls [293]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [294]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[295])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file notation.gls.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[296] (./names.ind [297] [298]) (./topologybook.ind</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.76491pt too wide) in paragraph at lines 21--23</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Baire Cat-e-gory The-o-rem, [][]185[][], [][]223[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.53792pt too wide) in paragraph at lines 34--35</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Bolzano-Weierstrass The-o-rem, [][]278[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.18558pt too wide) in paragraph at lines 35--37</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) bound (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20) b</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ounded; lower bound;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[299]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.28082pt too wide) in paragraph at lines 96--98</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) co-finite topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">m/n/10 (-20) finite-com-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (4.74039pt too wide) in paragraph at lines 110--111</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) and Haus-dorff space, [][]263[][]--[][]264[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (11.63974pt too wide) in paragraph at lines 125--127</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) space; order-completeness) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[300]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (4.49474pt too wide) in paragraph at lines 146--147</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) and con-ver-gent se-quence, [][]176[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.13008pt too wide) in paragraph at lines 149--150</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) from Eu-clidean $\OML/hlcm/m/it/10 n$\T1/hlh/m/n/10 (-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">20) -space to real</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.416pt too wide) in paragraph at lines 150--151</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) on com-pact met-ric space, [][]279[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.28401pt too wide) in paragraph at lines 167--168</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) of com-pact met-ric space, [][]279[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.44911pt too wide) in paragraph at lines 191--193</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/it/10 (-20) See also \T1/hlh/m/n/10 (-20) con-nected space; sep-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (17.60744pt too wide) in paragraph at lines 191--193</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) a-ra-tion; to-tally dis-con-nected</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.79329pt too wide) in paragraph at lines 216--217</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) distance-preserving map, [][]151[][], [][]152[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[301]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.3123pt too wide) in paragraph at lines 246--248</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Euclidean in-ner prod-uct, [][]158[][], [][]181[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.04117pt too wide) in paragraph at lines 270--271</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) extreme (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> max-i-mum,minimum) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.8835pt too wide) in paragraph at lines 283--285</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) first-category set (\T1/hlh/m/it/10 (-20) see \T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) mea-ger set) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[302]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.30344pt too wide) in paragraph at lines 324--326</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) Borel-Lebesgue The-o-rem) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.28027pt too wide) in paragraph at lines 326--327</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Heine-Borel-Lebesgue The-o-rem, [][]264[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (18.59972pt too wide) in paragraph at lines 350--351</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) see also \T1/hlh/m/n/10 (-20) e</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l-e-ment,member,subset) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.43198pt too wide) in paragraph at lines 363--365</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) tion,mathematical in-duc-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[303]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.584pt too wide) in paragraph at lines 394--395</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) of a collection of sets, [][]\T1/hlh/b/it/10 39[][]\T1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/hlh/m/n/10 (-20) , [][]39[][]--</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.77872pt too wide) in paragraph at lines 470--471</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) defined piecewise, [][]21[][]--[][]22[][], [][]38[][]-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[304]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.09427pt too wide) in paragraph at lines 496--498</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) ex-am-ples of, [][]99[][], [][]103[][]--[][]114[][], [</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">][]116[][],</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.06433pt too wide) in paragraph at lines 515--517</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) topo-log-i-cally equiv-a-lent, [][]\T1/hlh/b/it/10 154</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[][]\T1/hlh/m/n/10 (-20) ,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (8.51826pt too wide) in paragraph at lines 517--518</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) metrically equiv-a-lent met-ric spaces,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.2026pt too wide) in paragraph at lines 544--546</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) neighborhood, [][]\T1/hlh/b/it/10 200[][]\T1/hlh/m/n/10 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(-20) , [][]200[][]--[][]202[][], [][]228[][],</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.06833pt too wide) in paragraph at lines 555--557</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Niemytzki plane (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 (-20) tan-gent disk</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[305]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (9.05663pt too wide) in paragraph at lines 574--575</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) in second-countable space, [][]275[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.59937pt too wide) in paragraph at lines 592--593</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) and mul-ti-plica-tive in-verse, [][]20[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (4.32907pt too wide) in paragraph at lines 600--602</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) order topol-ogy, [][]\T1/hlh/b/it/10 235[][]\T1/hlh/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 (-20) , [][]235[][]--[][]236[][], [][]245[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.82869pt too wide) in paragraph at lines 609--611</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) der-ing; pre-order-ing; strict</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (20.25978pt too wide) in paragraph at lines 609--611</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) weak or-der-ing; well-ordering) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[306]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.26106pt too wide) in paragraph at lines 728--730</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) func-tional re-la-tion, or-der</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[307]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.88599pt too wide) in paragraph at lines 751--753</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) second-category set (\T1/hlh/m/it/10 (-20) see \T1/hlh/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">m/n/10 (-20) non-mea-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.02753pt too wide) in paragraph at lines 753--754</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) second-countable space, [][]\T1/hlh/b/it/10 239[][]\T1/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lh/m/n/10 (-20) , [][]239[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.32431pt too wide) in paragraph at lines 769--771</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) sequential com-pact-ness, [][]275[][], [][]277[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.40741pt too wide) in paragraph at lines 777--779</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) smaller topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n/10 (-20) coarser topol-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.25479pt too wide) in paragraph at lines 783--785</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) space (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20) t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">opo-log-i-cal space, met-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.31657pt too wide) in paragraph at lines 787--788</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) statement (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0) pred-i-cate,sentence) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.04988pt too wide) in paragraph at lines 788--790</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) strict or-der-ing (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n/10 (-20) strict di-rected</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.03561pt too wide) in paragraph at lines 788--790</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) or-der-ing; strict par-tial or-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.09906pt too wide) in paragraph at lines 792--794</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) stronger topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) finer topol-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[308]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (21.70116pt too wide) in paragraph at lines 850--852</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) topologically equiv-a-lent met-ric spaces,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.09372pt too wide) in paragraph at lines 862--863</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) gen-er-ated by a col-lec-tion, [][]234[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.37599pt too wide) in paragraph at lines 873--874</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) totally bounded met-ric space, [][]\T1/hlh/b/it/10 273[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.416pt too wide) in paragraph at lines 902--903</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) on com-pact met-ric space, [][]279[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[309]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.584pt too wide) in paragraph at lines 908--909</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) of a collection of sets, [][]\T1/hlh/b/it/10 39[][]\T1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/hlh/m/n/10 (-20) , [][]39[][]--</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (8.61229pt too wide) in paragraph at lines 935--937</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) weaker topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/10 (-20) coarser topol-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[310]))) (./topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file front/frontmatter.aux.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file front/preface.aux.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/chapterSetsMaps.aux) (./main/MetricSpaces/chapterMetrics.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/chapterTopological.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/chapterContinuityConvergence.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Compact/chapterCompact.aux) (./main/Connected/chapterConnected.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Embedding/chapterEmbedding.aux) (./back/backmatter.aux))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Dependency list written on topologybook.dep.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: There were undefined references.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">es not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@PinterSets2014} has been referenced but does</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@LakinsMathReasoning2016} has been referenced</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> but does not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@EisenbergMathMethod1996} has been referenced</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> but does not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">{/usr/local/texlive/2017/texmf-dist/fonts/enc/dvips/base/8r.enc}</Users/murray/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Library/texmf/fonts/type1/bh/lucida/lbd.pfb></Users/murray/Library/texmf/fonts/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">type1/bh/lucida/lbdi.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbma.pfb></Users/murray</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/Library/texmf/fonts/type1/bh/lucida/lbme.pfb></Users/murray/Library/texmf/font</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">s/type1/bh/lucida/lbmo.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/l</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">bmr.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbms.pfb></Users/mur</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ray/Library/texmf/fonts/type1/bh/lucida/lbmsd.pfb></Users/murray/Library/texmf/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fonts/type1/bh/lucida/lbr.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucid</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">a/lsd.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lsdi.pfb></Users/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">urray/Library/texmf/fonts/type1/bh/lucida/lsi.pfb></Users/murray/Library/texmf/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fonts/type1/bh/lucida/lsr.pfb></usr/local/texlive/2017/texmf-dist/fonts/type1/p</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ublic/xypic/xyatip10.pfb></usr/local/texlive/2017/texmf-dist/fonts/type1/public</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/xypic/xybtip10.pfb></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Output written on topologybook.pdf (316 pages, 1208256 bytes).</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">SyncTeX written on topologybook.synctex.gz.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Transcript written on topologybook.log.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'notation.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'names.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'topologybook.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'notation.gls' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file notation.gls.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'notation.gls' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file notation.gls.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Log file says output to 'topologybook.pdf'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Couldn't find aux file 'front/frontmatter.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Couldn't find aux file 'front/preface.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">=== TeX engine is 'pdfTeX'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Found bibliography file(s) [mytopologybook.bib mytopologyread.bib topologybook-blx.bib]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Summary of warnings:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Latex failed to resolve 9 reference(s)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'bibtex topologybook': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'back/backmatter.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Compact/chapterCompact.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Connected/chapterConnected.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/ContinuityConvergence/chapterContinuityConvergence.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Embedding/chapterEmbedding.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/MetricSpaces/chapterMetrics.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/SetsMaps/chapterSetsMaps.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/TopologicalSpaces/chapterTopological.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 3 of rule 'bibtex topologybook'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'bibtex "topologybook"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'bibtex topologybook'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">For rule 'bibtex topologybook', running '&run_bibtex( )' ...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is BibTeX, Version 0.99d (TeX Live 2017)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">The top-level auxiliary file: topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">The style file: biblatex.bst</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I couldn't open auxiliary file front/frontmatter.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">---line 25 of file topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : \@input{front/frontmatter.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : }</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I'm skipping whatever remains of this command</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I couldn't open auxiliary file front/preface.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">---line 39 of file topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : \@input{front/preface.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> : }</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">I'm skipping whatever remains of this command</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/SetsMaps/chapterSetsMaps.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/MetricSpaces/chapterMetrics.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/TopologicalSpaces/chapterTopological.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/ContinuityConvergence/chapterContinuityConvergence.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/Compact/chapterCompact.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/Connected/chapterConnected.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: main/Embedding/chapterEmbedding.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">A level-1 auxiliary file: back/backmatter.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Database file #1: topologybook-blx.bib</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Database file #2: mytopologybook.bib</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Database file #3: mytopologyread.bib</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Biblatex version: 3.3</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(There were 2 error messages)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: One or more aux files is missing for bibtex. I'll try</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> to get (pdf)latex to remake them.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Rule 'pdflatex': File changes, etc:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Changed files, or newly in use since previous run(s):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'back/backmatter.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Compact/chapterCompact.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Connected/chapterConnected.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/ContinuityConvergence/chapterContinuityConvergence.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/Embedding/chapterEmbedding.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/MetricSpaces/chapterMetrics.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/SetsMaps/chapterSetsMaps.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'main/TopologicalSpaces/chapterTopological.aux'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'topologybook.run.xml'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Run number 4 of rule 'pdflatex'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Running 'pdflatex --synctex=1 --file-line-error -recorder "topologybook.tex"'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">------------</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: applying rule 'pdflatex'...</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017) (preloaded format=pdflatex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> restricted \write18 enabled.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">entering extended mode</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX2e <2017-04-15></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Babel <3.12> and hyphenation patterns for 84 language(s) loaded.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/snapshot/snapshot.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/memoir.cls</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Document Class: memoir 2016/05/16 v3.7f configurable book, report, article docu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ment class</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ifpdf.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/ifetex/ifetex.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/plain/ifetex/ifetex.tex))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/ifxetex/ifxetex.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ifluatex.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/mem10.clo)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/mempatch.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/base/ifthen.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./preamble/preamble.tex (./preamble/packages.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/csquotes/csquotes.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/etoolbox/etoolbox.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/graphics/keyval.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/csquotes/csquotes.def)</div><div style="margin: 0px; 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/pgf/frontendlayer/tikz/librarie</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">s/tikzlibrarymatrix.code.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/pgf/frontendlayer/tikz/librarie</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">s/tikzlibraryquotes.code.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">meta.code.tex)))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/lipsum/lipsum.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./preamble/fonts.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/base/fontenc.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/cyrillic/ot2enc.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/base/t1enc.def))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucimatx/lucimatx.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/tools/bm.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/my/mymath.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/mathtools/mathtools.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/mathtools/mhsetup.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/centernot.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/scalerel/scalerel.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/my/mywidebar.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/my/myaccents.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Using mymath variant defs for Lucida Bright.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Using mymath variant defs for Lucida Bright.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (/Users/murray/Library/texmf/tex/generic/diagxy/diagxy.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xy.tex Bootstrap'ing:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">catcodes, docmode,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyrecat.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyidioms.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic version 3.8.9 <2013/10/06></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Copyright (c) 1991-2013 by Kristoffer H. Rose <<a href="mailto:krisrose@tug.org" class="">krisrose@tug.org</a>> and others</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic is free software: see the User's Guide for details.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Loading kernel: messages; fonts; allocations: state, direction,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">utility macros; pictures: \xy, positions, objects, decorations;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">kernel objects: directionals, circles, text; options; algorithms: directions,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">edges, connections; Xy-pic loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xyarrow.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic option: Arrow and Path feature v.3.9 path, \ar, loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/xypic/xycurve.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Xy-pic option: Curve and Spline extension v.3.12 curve, circles, loaded)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucida/t1hlh.fd))) (./preamble/style.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">******************************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Stock height and width: 794.96999pt by 614.295pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Top and edge trims: 0pt and 0pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Page height and width: 663pt by 456pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Text height and width: 538pt by 336pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Spine and edge margins: 60pt and 60pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Upper and lower margins: 67.5pt and 57.5pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Headheight and headsep: 12pt and 18.06749pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Footskip: 25.29494pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Columnsep and columnseprule: 10pt and 0pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Marginparsep and marginparwidth: 7pt and 46pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidecapsep and sidecapwidth: 7pt and 128pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidebarhsep and sidebarwidth: 7pt and 128pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidebarvsep and sidebartopsep: 12pt and 0pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidebarheight: 548.39996pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidefoothsep and sidefootwidth: 7pt and 128pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Sidefootvsep and sidefootheight: 12pt and 548.39996pt</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">******************************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucida/t1hls.fd))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./preamble/mathdefs.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/mathtools/empheq.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thmtools.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-patch.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/parseargs.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-kv.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/infwarerr.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/etexcmds.sty)))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-autoref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/aliasctr.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/carlisle/remreset.sty)))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-listof.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-restate.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thm-amsthm.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">****************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">>>> Made patch specific for amsthm.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">****************************************</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./preamble/links.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/biblatex.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ltxcmds.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/kvoptions.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/logreq/logreq.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/logreq/logreq.def))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/url/url.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/blx-dm.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/blx-compat.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/blx-bibtex.def</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Using fall-back BibTeX(8) backend:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) functionality may be reduced/unavailable.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/biblatex.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/biblatex/bbx/mybooknumeric.bbx</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/bbx/standard.bbx)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/bbx/numeric.bbx))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/cbx/numeric.cbx)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./biblatex.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/nomencl/nomencl.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Using the configuration file nomencl.cfg</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./nomencl.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/repeatindex/repeatindex.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/tools/afterpage.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/hyperref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/auxhook.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/pd1enc.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/latexconfig/hyperref.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/memhfixc.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Message: Driver (autodetected): hpdftex.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/hpdftex.def</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Option `pdftex' has already been used,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) setting the option has no effect on input line 107.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/xmpincl/xmpincl.sty)<<TopologyEd2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">metadata.xmpi>></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/hyperxmp/hyperxmp.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/stringenc.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/doclicense/doclicense.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/xifthen/xifthen.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/tools/xspace.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/doclicense/doclicense-english.ldf</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) (/usr/local/texlive/2017/texmf-dist/tex/latex/oberdiek/aliascnt.sty)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/cleveref/cleveref.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./preamble/labels.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/showlabels/showlabels.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package: `showlabels' v1.8 <2016/06/09></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">with amsmath equation tags</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">))) (/usr/local/texlive/2017/texmf-dist/tex/latex/microtype/microtype.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/microtype/microtype-pdftex.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/latex/microtype/microtype.cfg))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing nomenclature file topologybook.nlo</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing index file notation.idx </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing index file names.idx </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Writing index file topologybook.idx </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/biblatex/lbx/mylanguagestrings.lbx</div><div style="margin: 0px; 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">ABD: EveryShipout initializing macros (./topologybook.bbl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Biber reported the following issues</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) with 'Bernays1991':</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) - Can't use 'location' + 'address'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Biber reported the following issues</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) with 'KConradIsometries':</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) - Invalid format of field 'urldate'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Biber reported the following issues</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) with 'ChrisCooperIsometries':</div><div style="margin: 0px; font-size: 11px; 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font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Biber reported the following issues</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) with 'GaillardZorn2017':</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) - Invalid format of field 'urldate'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package biblatex Warning: Biber reported the following issues</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) with 'GraysonZorn2007':</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(biblatex) - Invalid format of field 'urldate'.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (/usr/local/texlive/2017/texmf-dist/tex/latex/hyperref/nameref.sty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/gettitlestring.sty))</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Redoing nameref's sectioning</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Redoing nameref's label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.out) (./topologybook.out)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/se-pdfdoc.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/se-utf8.def)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./topologybook.toc [1{/Users/murray/Library/texlive/2017/texmf-var/fonts/map/p</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">dftex/updmap/pdftex.map}]) [2] (./topologybook.toc [3] [4] [5]) [6]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/mainmatter.tex (./main/SetsMaps/chapterSetsMaps.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/setsmaps-init.tex) (./main/SetsMaps/logic.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [1])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/sets.tex [2] [3] [4] [5] [6]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucidabr/omshlh.fd) [7] [8] [9] [10]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[11] [12]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (38.67267pt too wide) in paragraph at lines 733--734</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) verse re-la-tion $[]$ is \T1/hlh/m/it/10 (-20) not \T1/hlh</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/m/n/10 (-20) func-tional be-cause the set $\OMS/hlcy/m/n/10 f [] g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[13] [14]) (./main/SetsMaps/maps.tex [15] [16] [17] [18] [19] [20] [21]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[22] [23] [24] [25] [26] [27] [28]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.20296pt too wide) in paragraph at lines 934--935</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) In examples ([][]*[][]) of the subsection ``Injections, </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">surjections, and bijections''</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[29] [30] [31]) (./main/SetsMaps/families.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 48.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 48.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[32]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 116.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 116.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[33] [34] [35] [36]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.7854pt too wide) in paragraph at lines 368--369</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) The union and in-ter-sec-tion of two sets in the sense o</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">f sub-sec-tion ``Union</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.96655pt too wide) in paragraph at lines 372--374</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) Moreover, the for-mu-las in-volv-ing union and in-ter-sec-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">tion in sub-sec-tion ``Union</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[37] [38] [39] [40] [41] [42] [43] [44]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.57535pt too wide) in paragraph at lines 909--910</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Let $\OML/hlcm/m/it/10 n$ \T1/hlh/m/n/10 (-20) be a pos-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">i-tive in-te-ger and let $\OML/hlcm/m/it/10 ÑX[]Ö[]$ \T1/hlh/m/n/10 (-20) be a </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fam-ily of \T1/hlh/m/it/10 (-20) nonempty</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[45]) (./main/SetsMaps/recursion.tex [46] [47] [48] [49] [50] [51] [52])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/countable.tex [53]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.3389pt too wide) in paragraph at lines 84--88</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) Hence the map ob-tained from $\OML/hlcm/m/it/10 h[]$ \T1/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lh/m/n/10 (-20) by re-strict-ing its do-main to $\OMS/hlcy/m/n/10 f\T1/hlh/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ; n;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> n \OMS/hlcy/m/n/10 Ç</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[54]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.72176pt too wide) in paragraph at lines 152--155</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Now let $\OML/hlcm/m/it/10 n \OMS/hlcy/m/n/10 ^^U \T1/hl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">h/m/n/10 (-20) 1$ and as-sume that each sub-set of $\OMS/hlcy/m/n/10 f\T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> n\OMS/hlcy/m/n/10 g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[55] [56] [57] [58] [59] [60] [61] [62] [63]) (./main/SetsMaps/ordering.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[79]) (./main/SetsMaps/ordercomplete.tex [80] [81] [82] [83])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/equivrel.tex [84]) (./main/SetsMaps/well-ordering.tex [85]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[86] [87] [88]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 300.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[89] [90] [91] [92]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 619.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[93]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.15701pt too wide) in paragraph at lines 727--728</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) The pre-ced-ing proof is a typ-i-cal pro-ce-dure for ap-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ply-ing Zorn's Lemma.To</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[94] [95])) [96] (./main/MetricSpaces/chapterMetrics.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/MetricSpaces/metrics-init.tex) (./main/MetricSpaces/metrics.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[97]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.58485pt too wide) in paragraph at lines 79--79</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[98] [99] [100] [101] [102]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `superscript' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(hyperref) removing `math shift' on input line 364.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[103]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.6}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.384 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:taxicab-metric} [104] [105]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(/Users/murray/Library/texmf/tex/latex/lucida/ts1hlh.fd) [106] [107]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (9.80023pt too wide) in paragraph at lines 624--625</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hls/b/n/10 1.9 Ex-am-ple. []\T1/hlh/m/n/10 (-20) Again let $\OML/hlcm/m/i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t/10 X$ \T1/hlh/m/n/10 (-20) be the set of all con-tin-u-ous func-tions $\OML/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lcm/m/it/10 x [] [] Ü\T1/hlh/m/n/10 (-20) 0\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-20) 1\OML/hlcm/m/it/10 á [] \LMR/hlcm/m/n/10 R$\T1/hlh/m/n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[108] [109] [110] [111] [112] [113] [114]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.90543pt too wide) in paragraph at lines 1092--1093</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Are the taxi-cab and max met-rics on $\LMR/hlcm/m/n/10 R</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]$ \T1/hlh/m/n/10 (-20) also translation-invariant?</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[115] [116] [117] [118]) (./main/MetricSpaces/openclosed.tex [119] [120]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[121] [122] [123] [124] [125] [126] [127] [128] [129] [130]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 2846) has occurred while \output is active [131]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[132] [133] [134]pdfTeX warning (ext4): destination with the same identifier (n</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ame{corollary.26}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.864 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:separate-pts-in-metric} [135] [136] [137] [138] [139] [140])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/MetricSpaces/equivalent.texpdfTeX warning (ext4): destination with the </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">same identifier (name{proposition.33}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.31 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:equiv-metrics-via-balls} [141]pdfTeX warning (ext4): destinati</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on with the same identifier (name{proposition.34}) has been already used, dupli</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">cate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.68 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:d-and-dmax-equiv} [142]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1454) has occurred while \output is active [143]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[144]pdfTeX warning (ext4): destination with the same identifier (name{proposit</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ion.38}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.250 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:bded-metric-equiv-to-given} [145] [146] [147] [148] [149]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[150]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.43}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.582 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:isometry} [151]pdfTeX warning (ext4): destination with the sam</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e identifier (name{examples.44}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.610 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:isometries}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (25.85425pt too wide) detected at line 643</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[152]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.61795pt too wide) detected at line 746</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\OML/hlcm/m/it/10 d[]Ñy[]; y[]Ö \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 d[][]fÑx[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Ö; fÑx[]Ö[] \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 dÑx[]; x[]Ö \OMS/hlcy/m/n/10 É</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \OML/hlcm/m/it/10 d[]f[]Ñy[]Ö; f[]Ñy[]Ö[]: []</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[153]pdfTeX warning (ext4): destination with the same identifier (name{definiti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">on.46}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.765 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:top-equiv-metric-spaces}pdfTeX warning (ext4): destination wit</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">h the same identifier (name{examples.47}) has been already used, duplicate igno</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">red</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.786 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:top-equiv-metric-spaces} [154]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (16.05836pt too wide) in paragraph at lines 831--832</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) The met-ric space $\OML/hlcm/m/it/10 ÑÜ\T1/hlh/m/n/10 (-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">20) 0\OML/hlcm/m/it/10 ; cá; dÖ$ \T1/hlh/m/n/10 (-20) is topo-log-i-cally equiv</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-a-lent to $\OML/hlcm/m/it/10 ÑÜa; bá; d[]Ö$\T1/hlh/m/n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (25.11824pt too wide) in paragraph at lines 843--846</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) ---the com-pos-ite of a trans-la-tion fol-lowed by a di-la</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-tion or contraction---</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[155] [156]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.39265pt too wide) in paragraph at lines 993--995</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Let $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) be the col</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-lec-tion of all nonempty $\OML/hlcm/m/it/10 d$\T1/hlh/m/n/10 (-20) -closed sub</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-sets of a bounded</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[157] [158]) (./main/MetricSpaces/contconv.texpdfTeX warning (ext4): destinatio</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n with the same identifier (name{definition.49}) has been already used, duplica</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">te ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.20 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:cont-metric} [159]pdfTeX warning (ext4): destination with the s</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ame identifier (name{examples.50}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.51 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:cont-metric} [160] [161]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.56319pt too wide) in paragraph at lines 181--181</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[162]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (21.48416pt too wide) in paragraph at lines 222--223</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/it/10 (-20) For each $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/it/10 (-20) -</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">neighborhood $\OML/hlcm/m/it/10 N$ \T1/hlh/m/it/10 (-20) of $\OML/hlcm/m/it/10 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">fÑxÖ$ \T1/hlh/m/it/10 (-20) in $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/it/10 (-20) ther</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e ex-ists some $\OML/hlcm/m/it/10 d$\T1/hlh/m/it/10 (-20) -neighborhood</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[163]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (8.2688pt too wide) in paragraph at lines 288--293</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Assume ([][]3[][]). Let $\OML/hlcm/m/it/10 " > \T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) 0$. Since $\OML/hlcm/m/it/10 B[]ÑfÑxÖ\T1/hlh/m/n/10 (-20) ; \OML/hl</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">cm/m/it/10 d[]Ö$ \T1/hlh/m/n/10 (-20) is a $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/n/1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0 (-20) -neighborhood</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[164] [165] [166] [167]pdfTeX warning (ext4): destination with the same identif</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ier (name{examples.59}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.527 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:seq-conv-metric} [168] [169] [170] [171] [172]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1097) has occurred while \output is active [173]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[174] [175] [176] [177]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.8464pt too wide) in paragraph at lines 1114--1116</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) of ad-di-tion and mul-ti-pli-ca-tion, re-spec-tively, are </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">$\OML/hlcm/m/it/10 Ñd[]; dÖ$\T1/hlh/m/n/10 (-20) -continuous. </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[178] [179] [180] [181] [182]) (./main/MetricSpaces/complete.tex [183] [184]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[185]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.25098pt too wide) in paragraph at lines 197--199</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) For ex-am-ple, any isom-e-try from $\OML/hlcm/m/it/10 ÑX; </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">dÖ$ \T1/hlh/m/n/10 (-20) and $\OML/hlcm/m/it/10 ÑY; d[]Ö$ \T1/hlh/m/n/10 (-20) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">is $\OML/hlcm/m/it/10 Ñd; d[]Ö$\T1/hlh/m/n/10 (-20) -uniformly</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">)) [186] (./main/TopologicalSpaces/chapterTopological.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/topological-init.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/topologies.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 5954) has occurred while \output is active [187]pdfTeX</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> warning (ext4): destination with the same identifier (name{definition.2}) has </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.59 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:topological-space} [188] [189] [190] [191] [192] [193] [194]pdf</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">TeX warning (ext4): destination with the same identifier (name{proposition.11})</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.505 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> [195] [196] [197] [198]) (./main/TopologicalSpaces/neighborhoods.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[199] [200]pdfTeX warning (ext4): destination with the same identifier (name{pr</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">oposition.15}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.112 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:open-iff-nbd-each-pt}pdfTeX warning (ext4): destination with </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">the same identifier (name{definition.16}) has been already used, duplicate igno</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">red</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.123 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:nbd-of-set} [201] [202] [203] [204]pdfTeX warning (ext4): dest</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ination with the same identifier (name{examples.21}) has been already used, dup</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">licate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.322 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:hausdorff-spaces} [205] [206] [207] [208] [209]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (11.06798pt too wide) in paragraph at lines 855--856</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) Note: \T1/hlh/m/n/10 (-20) A reg-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">u-lar space, even a reg-u-lar $\OML/hlcm/m/it/10 T[]$\T1/hlh/m/n/10 (-20) -spac</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e, need not be metrizable---</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[210]) (./main/TopologicalSpaces/boundary.tex [211] [212] [213] [214]pdfTeX war</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ning (ext4): destination with the same identifier (name{definition.27}) has bee</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.283 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> pdfTeX warning (ext4): destination with the same identifier (name{proposi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">tion.28}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.315 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:interior-pt-via-nbds} [215] [216]pdfTeX warning (ext4): desti</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nation with the same identifier (name{corollary.31}) has been already used, dup</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">licate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.430 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:open-iff-equals-interior} [217] [218] [219] [220]pdfTeX warnin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">g (ext4): destination with the same identifier (name{corollary.41}) has been al</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ready used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.802 F</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> or every subset $A$ of a topological space $X$: [221] [222]pdfTeX warnin</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">g (ext4): destination with the same identifier (name{definition.45}) has been a</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lready used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.962 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:nowhere-dense}pdfTeX warning (ext4): destination with the same</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> identifier (name{definition.46}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.989 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:meager set} [223] [224] [225]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `cref' on page 226 undefined on input line 1201.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `ex:right-interval-topology-R' on page 1 undefined on </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">input line 1201.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[226] [227]) (./main/TopologicalSpaces/bases.tex [228] [229]pdfTeX warning (ext</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">4): destination with the same identifier (name{definition.53}) has been already</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.165 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:1st-countable} [230] [231]pdfTeX warning (ext4): destination w</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ith the same identifier (name{definition.55}) has been already used, duplicate </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.253 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:base}pdfTeX warning (ext4): destination with the same identifi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">er (name{examples.56}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.278 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:bases} [232] [233] [234]pdfTeX warning (ext4): destination with</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> the same identifier (name{examples.59}) has been already used, duplicate ignor</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.508 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:top-from-base} [235]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 650.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[236]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (15.12009pt too wide) in paragraph at lines 676--701</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) de-picts three mem-bers of a set of the form $\OML/hlcm/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">it/10 B[]x[]; x[]; x[]; x[] \T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[];</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> I[]; I[][]$\T1/hlh/m/n/10 (-20) .]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (39.92242pt too wide) in paragraph at lines 676--701</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \T1/hlh/m/n/10 (-20) De-fine $\OMS/hlcy/m/n/10 B$ \T1/hlh/m/n/10 (-20) to be t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">he col-lec-tion of all such sub-sets $\OML/hlcm/m/it/10 B[]x[]; x[]; [] ; x[] \</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[]; [] ; I[][]$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (15.45676pt too wide) in paragraph at lines 676--701</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) of $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) for all pos-s</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">i-ble choices of $\OML/hlcm/m/it/10 k$\T1/hlh/m/n/10 (-20) , of $\OML/hlcm/m/it</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/10 Ñ[]Ö$\T1/hlh/m/n/10 (-20) , and of $\OML/hlcm/m/it/10 Ñ[]Ö$\T1/hlh/m/n/10 (</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[237]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 5985) has occurred while \output is active [238]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[239]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 2828) has occurred while \output is active [240]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[241]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 1448) has occurred while \output is active [242]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[243] [244] [245])) [246]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/chapterContinuityConvergence.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/continuityconvergence-init.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/continuous.tex [247]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (13.0625pt too wide) in paragraph at lines 56--59</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/10 S\OML/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$ \T1/hlh/m/n/10 (-2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0) is also con-tin-u-ous as a map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 T\OML/hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$\T1/hlh/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n/10 (-20) .</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/ContinuityConvergence/homeomorphism.tex [248])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/productspace.tex [249] [250]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 128.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/ContinuityConvergence/quotientspace.tex [251])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/ContinuityConvergence/convergence.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `thm:WHAT' on page 1 undefined on input line 8.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{proposition.5</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.35 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:unif-conv-implies-ptwise-conv} [252])) [253]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Compact/chapterCompact.tex [254] (./main/Compact/compact-init.tex)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Compact/compact.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [255]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[256] [257] [258]pdfTeX warning (ext4): destination with the same identifier (n</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ame{definition.5}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.218 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:cpt}pdfTeX warning (ext4): destination with the same identifie</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">r (name{examples.6}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.241 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:cpt-spaces} [259] [260]pdfTeX warning (ext4): destination with </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">the same identifier (name{definition.7}) has been already used, duplicate ignor</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ed</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.367 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:fip} [261]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `hm:unit-interval-compact' on page 1 undefined on inpu</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">t line 457.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[262] [263]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Package thmtools Warning: Unused key `refname' on input line 544.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{example.15}) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.568 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:Cantor-K} [264]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Command \i invalid in math mode on input line 612.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Command \i invalid in math mode on input line 612.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[265]pdfTeX warning (ext4): destination with the same identifier (name{corollar</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">y.20}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.698 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:quotient-of-cpt-is-cpt}pdfTeX warning (ext4): destination with</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> the same identifier (name{corollary.21}) has been already used, duplicate igno</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">red</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.706 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:homeomorph-of-cpt-is-cpt}pdfTeX warning (ext4): destination wi</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">th the same identifier (name{corollary.22}) has been already used, duplicate ig</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">nored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.725 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:cont-from-cpt-to-T2-is-closed} [266] [267] [268] [269]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[270]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.73897pt too wide) in paragraph at lines 1010--1012</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) log-i-cal space $\OML/hlcm/m/it/10 X$ \T1/hlh/m/n/10 (-20)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> to a com-pact space $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/n/10 (-20) whose graph $[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[271]) (./main/Compact/compactmetric.tex [272]pdfTeX warning (ext4): destinatio</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n with the same identifier (name{proposition.36}) has been already used, duplic</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.103 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:cpt-metrizable-is-totally-bded}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [273]pdfTe</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">X warning (ext4): destination with the same identifier (name{examples.37}) has </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.131 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:totally-bded}pdfTeX warning (ext4): destination with the same i</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">dentifier (name{proposition.38}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.182 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {prop:totally-bded-is-2nd-countable} [274] [275] [276]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 345.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 347.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 347.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.42</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.385 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:limit-pt}pdfTeX warning (ext4): destination with the same iden</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">tifier (name{corollary.43}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.394 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {cor:limit-pt-in-cpt-metrizable} [277] [278] [279] [280]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (49.65659pt too wide) in paragraph at lines 660--662</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) [\T1/hlh/m/it/10 (-20) Hint: \T1/hlh/m/n/10 (-20) Form t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">he col-lec-tion $\OMS/hlcy/m/n/10 f [] g$ \T1/hlh/m/n/10 (-20) where $\OML/hlcm</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/m/it/10 E[] \OMS/hlcy/m/n/10 É f [] g$</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/Compact/locallycompact.tex)) [281]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Connected/chapterConnected.tex [282]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Connected/connected-init.tex) (./main/Connected/connected.texpdfTeX war</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ning (ext4): destination with the same identifier (name{definition.1}) has been</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.12 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:connected} [283]pdfTeX warning (ext4): destination with the sam</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e identifier (name{lemma.4}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.71 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {lem:conn-in-open-closed-it-meets}) (./main/Connected/components.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (ext4): destination with the same identifier (name{definition.5}</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.15 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:component} [284]pdfTeX warning (ext4): destination with the sam</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">e identifier (name{definition.8}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.76 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {def:totally-disconnected} [285]pdfTeX warning (ext4): destination w</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ith the same identifier (name{examples.9}) has been already used, duplicate ign</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.90 \label</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> {ex:totally-disconnected} [286]) (./main/Connected/pathconnected.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">) (./main/Connected/homotopy.tex) (./main/Connected/simplyconnected.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[287])) [288] (./main/Embedding/chapterEmbedding.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/Embedding/separation.tex) (./main/Embedding/metrization.texpdfTeX warni</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ng (ext4): destination with the same identifier (name{proposition.1}) has been </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.12 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> pdfTeX warning (ext4): destination with the same identifier (name{namedthe</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">orem.2}) has been already used, duplicate ignored</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""><to be read again> </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> \relax </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l.30 ...theorem}[name=Urysohn Metrization Theorem]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> [289])) [290])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./back/backmatter.tex (./back/exerciseguide.tex</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 23--23</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 23--25</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 27--27</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 27--29</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 31--31</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 31--33</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 35--35</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 35--37</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 39--39</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 39--41</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 42--42</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 42--44</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 46--46</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 46--48</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 50--50</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 50--52</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 54--54</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 54--56</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 58--58</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 58--60</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 62--62</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 62--64</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 66--66</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 66--68</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 70--70</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 70--72</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 74--74</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 74--76</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 1173) in paragraph at lines 78--78</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) 2.99, 2.99, 2.99, 2.99, 2.99,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \hbox (badness 10000) in paragraph at lines 78--80</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]|\T1/hlh/m/n/10 (+20) pages 235--999,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[291] [292]) (./back/indexes.tex (./topologybook.nls [293]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Underfull \vbox (badness 10000) has occurred while \output is active [294]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[295])</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file notation.gls.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[296] (./names.ind [297] [298]) (./topologybook.ind</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.76491pt too wide) in paragraph at lines 21--23</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Baire Cat-e-gory The-o-rem, [][]185[][], [][]223[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.53792pt too wide) in paragraph at lines 34--35</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Bolzano-Weierstrass The-o-rem, [][]278[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.18558pt too wide) in paragraph at lines 35--37</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) bound (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20) b</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">ounded; lower bound;</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[299]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.28082pt too wide) in paragraph at lines 96--98</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) co-finite topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">m/n/10 (-20) finite-com-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (4.74039pt too wide) in paragraph at lines 110--111</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) and Haus-dorff space, [][]263[][]--[][]264[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (11.63974pt too wide) in paragraph at lines 125--127</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) space; order-completeness) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[300]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (4.49474pt too wide) in paragraph at lines 146--147</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) and con-ver-gent se-quence, [][]176[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.13008pt too wide) in paragraph at lines 149--150</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) from Eu-clidean $\OML/hlcm/m/it/10 n$\T1/hlh/m/n/10 (-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">20) -space to real</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.416pt too wide) in paragraph at lines 150--151</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) on com-pact met-ric space, [][]279[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.28401pt too wide) in paragraph at lines 167--168</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) of com-pact met-ric space, [][]279[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.44911pt too wide) in paragraph at lines 191--193</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/it/10 (-20) See also \T1/hlh/m/n/10 (-20) con-nected space; sep-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (17.60744pt too wide) in paragraph at lines 191--193</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) a-ra-tion; to-tally dis-con-nected</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.79329pt too wide) in paragraph at lines 216--217</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) distance-preserving map, [][]151[][], [][]152[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[301]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.3123pt too wide) in paragraph at lines 246--248</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Euclidean in-ner prod-uct, [][]158[][], [][]181[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.04117pt too wide) in paragraph at lines 270--271</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) extreme (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> max-i-mum,minimum) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.8835pt too wide) in paragraph at lines 283--285</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) first-category set (\T1/hlh/m/it/10 (-20) see \T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) mea-ger set) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[302]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.30344pt too wide) in paragraph at lines 324--326</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) Borel-Lebesgue The-o-rem) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.28027pt too wide) in paragraph at lines 326--327</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Heine-Borel-Lebesgue The-o-rem, [][]264[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (18.59972pt too wide) in paragraph at lines 350--351</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) see also \T1/hlh/m/n/10 (-20) e</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">l-e-ment,member,subset) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.43198pt too wide) in paragraph at lines 363--365</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) tion,mathematical in-duc-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[303]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.584pt too wide) in paragraph at lines 394--395</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) of a collection of sets, [][]\T1/hlh/b/it/10 39[][]\T1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/hlh/m/n/10 (-20) , [][]39[][]--</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.77872pt too wide) in paragraph at lines 470--471</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) defined piecewise, [][]21[][]--[][]22[][], [][]38[][]-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[304]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.09427pt too wide) in paragraph at lines 496--498</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) ex-am-ples of, [][]99[][], [][]103[][]--[][]114[][], [</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">][]116[][],</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.06433pt too wide) in paragraph at lines 515--517</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) topo-log-i-cally equiv-a-lent, [][]\T1/hlh/b/it/10 154</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[][]\T1/hlh/m/n/10 (-20) ,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (8.51826pt too wide) in paragraph at lines 517--518</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) metrically equiv-a-lent met-ric spaces,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.2026pt too wide) in paragraph at lines 544--546</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) neighborhood, [][]\T1/hlh/b/it/10 200[][]\T1/hlh/m/n/10 </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(-20) , [][]200[][]--[][]202[][], [][]228[][],</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.06833pt too wide) in paragraph at lines 555--557</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) Niemytzki plane (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 (-20) tan-gent disk</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[305]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (9.05663pt too wide) in paragraph at lines 574--575</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) in second-countable space, [][]275[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.59937pt too wide) in paragraph at lines 592--593</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) and mul-ti-plica-tive in-verse, [][]20[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (4.32907pt too wide) in paragraph at lines 600--602</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) order topol-ogy, [][]\T1/hlh/b/it/10 235[][]\T1/hlh/m/n/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">10 (-20) , [][]235[][]--[][]236[][], [][]245[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (5.82869pt too wide) in paragraph at lines 609--611</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) der-ing; pre-order-ing; strict</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (20.25978pt too wide) in paragraph at lines 609--611</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) weak or-der-ing; well-ordering) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[306]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.26106pt too wide) in paragraph at lines 728--730</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) func-tional re-la-tion, or-der</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[307]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.88599pt too wide) in paragraph at lines 751--753</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) second-category set (\T1/hlh/m/it/10 (-20) see \T1/hlh/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">m/n/10 (-20) non-mea-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.02753pt too wide) in paragraph at lines 753--754</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) second-countable space, [][]\T1/hlh/b/it/10 239[][]\T1/h</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">lh/m/n/10 (-20) , [][]239[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.32431pt too wide) in paragraph at lines 769--771</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) sequential com-pact-ness, [][]275[][], [][]277[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (10.40741pt too wide) in paragraph at lines 777--779</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) smaller topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n/10 (-20) coarser topol-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (1.25479pt too wide) in paragraph at lines 783--785</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) space (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20) t</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">opo-log-i-cal space, met-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (6.31657pt too wide) in paragraph at lines 787--788</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) statement (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-2</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">0) pred-i-cate,sentence) </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.04988pt too wide) in paragraph at lines 788--790</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) strict or-der-ing (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">n/10 (-20) strict di-rected</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.03561pt too wide) in paragraph at lines 788--790</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">\T1/hlh/m/n/10 (-20) or-der-ing; strict par-tial or-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (3.09906pt too wide) in paragraph at lines 792--794</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) stronger topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/n/10 (-20) finer topol-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[308]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (21.70116pt too wide) in paragraph at lines 850--852</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) topologically equiv-a-lent met-ric spaces,</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.09372pt too wide) in paragraph at lines 862--863</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) gen-er-ated by a col-lec-tion, [][]234[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.37599pt too wide) in paragraph at lines 873--874</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) totally bounded met-ric space, [][]\T1/hlh/b/it/10 273[]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (2.416pt too wide) in paragraph at lines 902--903</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) on com-pact met-ric space, [][]279[][] </div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[309]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (0.584pt too wide) in paragraph at lines 908--909</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]| \T1/hlh/m/n/10 (-20) of a collection of sets, [][]\T1/hlh/b/it/10 39[][]\T1</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/hlh/m/n/10 (-20) , [][]39[][]--</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Overfull \hbox (8.61229pt too wide) in paragraph at lines 935--937</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[]\T1/hlh/m/n/10 (-20) weaker topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">/10 (-20) coarser topol-</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">[310]))) (./topologybook.aux</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file front/frontmatter.aux.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">No file front/preface.aux.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/SetsMaps/chapterSetsMaps.aux) (./main/MetricSpaces/chapterMetrics.aux)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">(./main/TopologicalSpaces/chapterTopological.aux)</div><div style="margin: 0px; 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font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">pdfTeX warning (dest): name{cite.0@EisenbergMathMethod1996} has been referenced</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> but does not exist, replaced by a fixed one</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco; min-height: 15px;" class=""><br class=""></div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">{/usr/local/texlive/2017/texmf-dist/fonts/enc/dvips/base/8r.enc}</Users/murray/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Library/texmf/fonts/type1/bh/lucida/lbd.pfb></Users/murray/Library/texmf/fonts/</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">type1/bh/lucida/lbdi.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbi</div><div style="margin: 0px; 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line-height: normal; font-family: Monaco;" class="">SyncTeX written on topologybook.synctex.gz.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Transcript written on topologybook.log.</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'notation.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'names.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Index file 'topologybook.idx' was written</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/preface.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/preface.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'notation.gls' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file notation.gls.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'notation.gls' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file notation.gls.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">===========Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Missing input file: 'front/frontmatter.aux' from line</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> 'No file front/frontmatter.aux.'</div><div style="margin: 0px; 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font-size: 11px; line-height: normal; font-family: Monaco;" class="">=== TeX engine is 'pdfTeX'</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Found bibliography file(s) [mytopologybook.bib mytopologyread.bib topologybook-blx.bib]</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: Summary of warnings:</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class=""> Latex failed to resolve 9 reference(s)</div><div style="margin: 0px; font-size: 11px; line-height: normal; font-family: Monaco;" class="">Latexmk: All targets (topologybook.pdf) are up-to-date</div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""> =========== END console file ================</div><div class=""><div class="">
---<br class="">Murray Eisenberg<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="mailto:murrayeisenberg@gmail.com" class="">murrayeisenberg@gmail.com</a><br class="">503 King Farm Blvd #101<span class="Apple-tab-span" style="white-space: pre;"> </span>Home (240)-246-7240<br class="">Rockville, MD 20850-6667<span class="Apple-tab-span" style="white-space: pre;"> </span>Mobile (413)-427-5334<br class=""><br class="">
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<br class=""></div></div></div></blockquote></div><br class=""><div class="">
---<br class="">Murray Eisenberg<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="mailto:murrayeisenberg@gmail.com" class="">murrayeisenberg@gmail.com</a><br class="">503 King Farm Blvd #101<span class="Apple-tab-span" style="white-space: pre;"> </span>Home (240)-246-7240<br class="">Rockville, MD 20850-6667<span class="Apple-tab-span" style="white-space: pre;"> </span>Mobile (413)-427-5334<br class=""><br class="">
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