[OS X TeX] very slow pdflatexmk runs after upgrade TeXShop to 3.80
Murray Eisenberg
murrayeisenberg at gmail.com
Fri Jul 14 11:20:43 EDT 2017
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.
============== BEGIN ~/Library/TeXShop/bin/latexmkrcedit ===================
# Don't edit this file IF it is named latexmkrcDONTedit directly since
# TeXShop may replace it on update.
# If you wish to edit or add to this file, copy it to ~/Library/TeXShop/bin
# and rename it latexmkrcedit if that file doesn't already exist.
# Edit this File to add/change dependencies and rules
# The following is used by ALL the latexmk engine files
# change '--shell-escape' to an empty string, '', to remove the shell-escape default
#$TSUserCompileOptions = '--shell-escape';
$TSUserCompileOptions = '';
# turn recorder option off (no .fls file generated)
#$recorder=0;
# turn off duplicated missing references
$silence_logfile_warnings = 1;
# Custom dependency for glossaries package
# if you make custom glossaries you may have to add items to the @cus_dep_list and corresponding sub-routines
# NOTE: fileparse and $$Psource are undocumented latexmk as of version 4.40 --- Thanks to John Collins
# if you use the glossary package and DON'T use the glossaries package uncomment (remove the leading #)
# the single line with the system call and comment out (add leading #s) to the two following lines. No
# other changes are necessary. If you use both packages, place any project using the glossary package
# into a folder by itself and create a platexmkrc file containing the lines
# sub makeglo2gls {
# system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");
# }
# (without the leading #s) in that folder.
add_cus_dep('glo', 'gls', 0, 'makeglo2gls');
sub makeglo2gls {
# system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");
my ($name, $path) = fileparse($$Psource);
return system("makeglossaries -d '$path' '$name'");
}
# The glossaries package, with the [acronym] option, produces a .acn file when processed with (xe/pdf)latex and
# then makeindex/xindy to process the .acn into .acr and finally runs of (xe/pdf)latex to read in the .acr file.
add_cus_dep('acn', 'acr', 0, 'makeacn2acr');
sub makeacn2acr {
# system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acr '$_[0]'.acn");
my ($name, $path) = fileparse($$Psource);
return system("makeglossaries -d '$path' '$name'");
}
# example of an added custom glossary type that is used in some of the glossaries example files:
# this is for the new glossary type command \newglossary[nlg]{notation}{not}{ntn}{Notation} from the glossaries package
add_cus_dep('ntn', 'not', 0, 'makeacn2acr');
# for other glossaries 4.xx examples
add_cus_dep('flo', 'flx', 0, 'makeacn2acr');
add_cus_dep('acn2', 'acr2', 0, 'makeacn2acr');
# the glossary package samples do acr->acn and not->ntn rather than the reverse for the glossaries package
add_cus_dep('acr', 'acn', 0, 'makeacr2acn');
sub makeacr2acn {
system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acn '$_[0]'.acr");
}
add_cus_dep('not', 'ntn', 0, 'makenot2ntn');
sub makenot2ntn {
system("makeindex -s '$_[0]'.ist -t '$_[0]'.nlg -o '$_[0]'.ntn '$_[0]'.not");
}
# dependencies for custom indexes using the index package
# examples for sample.tex for index package:
add_cus_dep('adx', 'and', 0, 'makeadx2and');
sub makeadx2and {
system("makeindex -o '$_[0]'.and '$_[0]'.adx");
}
add_cus_dep('ndx', 'nnd', 0, 'makendx2nnd');
sub makendx2nnd {
system("makeindex -o '$_[0]'.nnd '$_[0]'.ndx");
}
add_cus_dep('ldx', 'lnd', 0, 'makeldx2lnd');
sub makeldx2lnd {
system("makeindex -o '$_[0]'.lnd '$_[0]'.ldx");
}
# dependency for biblatex example with a title index
add_cus_dep('tdx', 'tnd', 0, 'maketdx2tnd');
sub maketdx2tnd {
system("makeindex -o '$_[0]'.tnd '$_[0]'.tdx");
}
# Custom dependency and function for nomencl package
add_cus_dep('nlo', 'nls', 0, 'makenlo2nls');
sub makenlo2nls {
system("makeindex -s nomencl.ist -o '$_[0]'.nls '$_[0]'.nlo");
}
# Specify custom index style file:
#$makeindex = "makeindex -s my.ist %O -o %D %S”;
============== END ~/Library/TeXShop/bin/latexmkrcedit ===================
> On Jul 14, 2017, at 10:45 AM, Murray Eisenberg <murrayeisenberg at gmail.com> wrote:
>
> 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).
>
> 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.
>
> With the previous version, pdflatexmk typesetting ran smoothly, with none of the hiccuping stops now occurring.
>
> My pdflatexmkrc file and contents of the console are listed below.
>
>
> =========== BEGIN ~/Library/TewXShop/bin/tslatexmk/pdflatexmkrc =============
> # Don't edit this file IF it is named latexmkrcDONTedit directly since
> # TeXShop may replace it on update.
> # If you wish to edit or add to this file, copy it to ~/Library/TeXShop/bin
> # and rename it latexmkrcedit if that file doesn't already exist.
>
> # Edit this File to add/change dependencies and rules
> # The following is used by ALL the latexmk engine files
>
> # change '--shell-escape' to an empty string, '', to remove the shell-escape default
> #$TSUserCompileOptions = '--shell-escape';
> $TSUserCompileOptions = '';
>
> # turn recorder option off (no .fls file generated)
> #$recorder=0;
>
> # turn off duplicated missing references
> $silence_logfile_warnings = 1;
>
> # Custom dependency for glossaries package
> # if you make custom glossaries you may have to add items to the @cus_dep_list and corresponding sub-routines
> # NOTE: fileparse and $$Psource are undocumented latexmk as of version 4.40 --- Thanks to John Collins
> # if you use the glossary package and DON'T use the glossaries package uncomment (remove the leading #)
> # the single line with the system call and comment out (add leading #s) to the two following lines. No
> # other changes are necessary. If you use both packages, place any project using the glossary package
> # into a folder by itself and create a platexmkrc file containing the lines
> # sub makeglo2gls {
> # system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");
> # }
> # (without the leading #s) in that folder.
> add_cus_dep('glo', 'gls', 0, 'makeglo2gls');
> sub makeglo2gls {
> # system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");
> my ($name, $path) = fileparse($$Psource);
> return system("makeglossaries -d '$path' '$name'");
> }
> # The glossaries package, with the [acronym] option, produces a .acn file when processed with (xe/pdf)latex and
> # then makeindex/xindy to process the .acn into .acr and finally runs of (xe/pdf)latex to read in the .acr file.
> add_cus_dep('acn', 'acr', 0, 'makeacn2acr');
> sub makeacn2acr {
> # system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acr '$_[0]'.acn");
> my ($name, $path) = fileparse($$Psource);
> return system("makeglossaries -d '$path' '$name'");
> }
> # example of an added custom glossary type that is used in some of the glossaries example files:
> # this is for the new glossary type command \newglossary[nlg]{notation}{not}{ntn}{Notation} from the glossaries package
> add_cus_dep('ntn', 'not', 0, 'makeacn2acr');
> # for other glossaries 4.xx examples
> add_cus_dep('flo', 'flx', 0, 'makeacn2acr');
> add_cus_dep('acn2', 'acr2', 0, 'makeacn2acr');
>
> # the glossary package samples do acr->acn and not->ntn rather than the reverse for the glossaries package
> add_cus_dep('acr', 'acn', 0, 'makeacr2acn');
> sub makeacr2acn {
> system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acn '$_[0]'.acr");
> }
> add_cus_dep('not', 'ntn', 0, 'makenot2ntn');
> sub makenot2ntn {
> system("makeindex -s '$_[0]'.ist -t '$_[0]'.nlg -o '$_[0]'.ntn '$_[0]'.not");
> }
>
> # dependencies for custom indexes using the index package
> # examples for sample.tex for index package:
> add_cus_dep('adx', 'and', 0, 'makeadx2and');
> sub makeadx2and {
> system("makeindex -o '$_[0]'.and '$_[0]'.adx");
> }
> add_cus_dep('ndx', 'nnd', 0, 'makendx2nnd');
> sub makendx2nnd {
> system("makeindex -o '$_[0]'.nnd '$_[0]'.ndx");
> }
> add_cus_dep('ldx', 'lnd', 0, 'makeldx2lnd');
> sub makeldx2lnd {
> system("makeindex -o '$_[0]'.lnd '$_[0]'.ldx");
> }
>
> # dependency for biblatex example with a title index
> add_cus_dep('tdx', 'tnd', 0, 'maketdx2tnd');
> sub maketdx2tnd {
> system("makeindex -o '$_[0]'.tnd '$_[0]'.tdx");
> }
>
> # Custom dependency and function for nomencl package
> add_cus_dep('nlo', 'nls', 0, 'makenlo2nls');
> sub makenlo2nls {
> system("makeindex -s nomencl.ist -o '$_[0]'.nls '$_[0]'.nlo");
> }
>
> # Specify custom index style file:
> #$makeindex = "makeindex -s my.ist %O -o %D %S";# Don't edit this file IF it is named latexmkrcDONTedit directly since
> # TeXShop may replace it on update.
> # If you wish to edit or add to this file, copy it to ~/Library/TeXShop/bin
> # and rename it latexmkrcedit if that file doesn't already exist.
>
> # Edit this File to add/change dependencies and rules
> # The following is used by ALL the latexmk engine files
>
> # change '--shell-escape' to an empty string, '', to remove the shell-escape default
> #$TSUserCompileOptions = '--shell-escape';
> $TSUserCompileOptions = '';
>
> # turn recorder option off (no .fls file generated)
> #$recorder=0;
>
> # turn off duplicated missing references
> $silence_logfile_warnings = 1;
>
> # Custom dependency for glossaries package
> # if you make custom glossaries you may have to add items to the @cus_dep_list and corresponding sub-routines
> # NOTE: fileparse and $$Psource are undocumented latexmk as of version 4.40 --- Thanks to John Collins
> # if you use the glossary package and DON'T use the glossaries package uncomment (remove the leading #)
> # the single line with the system call and comment out (add leading #s) to the two following lines. No
> # other changes are necessary. If you use both packages, place any project using the glossary package
> # into a folder by itself and create a platexmkrc file containing the lines
> # sub makeglo2gls {
> # system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");
> # }
> # (without the leading #s) in that folder.
> add_cus_dep('glo', 'gls', 0, 'makeglo2gls');
> sub makeglo2gls {
> # system("makeindex -s '$_[0]'.ist -t '$_[0]'.glg -o '$_[0]'.gls '$_[0]'.glo");
> my ($name, $path) = fileparse($$Psource);
> return system("makeglossaries -d '$path' '$name'");
> }
> # The glossaries package, with the [acronym] option, produces a .acn file when processed with (xe/pdf)latex and
> # then makeindex/xindy to process the .acn into .acr and finally runs of (xe/pdf)latex to read in the .acr file.
> add_cus_dep('acn', 'acr', 0, 'makeacn2acr');
> sub makeacn2acr {
> # system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acr '$_[0]'.acn");
> my ($name, $path) = fileparse($$Psource);
> return system("makeglossaries -d '$path' '$name'");
> }
> # example of an added custom glossary type that is used in some of the glossaries example files:
> # this is for the new glossary type command \newglossary[nlg]{notation}{not}{ntn}{Notation} from the glossaries package
> add_cus_dep('ntn', 'not', 0, 'makeacn2acr');
> # for other glossaries 4.xx examples
> add_cus_dep('flo', 'flx', 0, 'makeacn2acr');
> add_cus_dep('acn2', 'acr2', 0, 'makeacn2acr');
>
> # the glossary package samples do acr->acn and not->ntn rather than the reverse for the glossaries package
> add_cus_dep('acr', 'acn', 0, 'makeacr2acn');
> sub makeacr2acn {
> system("makeindex -s '$_[0]'.ist -t '$_[0]'.alg -o '$_[0]'.acn '$_[0]'.acr");
> }
> add_cus_dep('not', 'ntn', 0, 'makenot2ntn');
> sub makenot2ntn {
> system("makeindex -s '$_[0]'.ist -t '$_[0]'.nlg -o '$_[0]'.ntn '$_[0]'.not");
> }
>
> # dependencies for custom indexes using the index package
> # examples for sample.tex for index package:
> add_cus_dep('adx', 'and', 0, 'makeadx2and');
> sub makeadx2and {
> system("makeindex -o '$_[0]'.and '$_[0]'.adx");
> }
> add_cus_dep('ndx', 'nnd', 0, 'makendx2nnd');
> sub makendx2nnd {
> system("makeindex -o '$_[0]'.nnd '$_[0]'.ndx");
> }
> add_cus_dep('ldx', 'lnd', 0, 'makeldx2lnd');
> sub makeldx2lnd {
> system("makeindex -o '$_[0]'.lnd '$_[0]'.ldx");
> }
>
> # dependency for biblatex example with a title index
> add_cus_dep('tdx', 'tnd', 0, 'maketdx2tnd');
> sub maketdx2tnd {
> system("makeindex -o '$_[0]'.tnd '$_[0]'.tdx");
> }
>
> # Custom dependency and function for nomencl package
> add_cus_dep('nlo', 'nls', 0, 'makenlo2nls');
> sub makenlo2nls {
> system("makeindex -s nomencl.ist -o '$_[0]'.nls '$_[0]'.nlo");
> }
>
> # Specify custom index style file:
> #$makeindex = "makeindex -s my.ist %O -o %D %S”;
>
> =========== END ~/Library/TewXShop/bin/tslatexmk/pdflatexmkrc =============
>
> =========== BEGIN console file ===============
>
> Subroutine makeglo2gls redefined at (eval 9) line 2, <GEN2> chunk 1.
> Latexmk: This is Latexmk, John Collins, 16 May 2017, version: 4.53a.
> Rule 'pdflatex': Rules & subrules not known to be previously run:
> pdflatex
> Rule 'pdflatex': The following rules & subrules became out-of-date:
> 'pdflatex'
> ------------
> Run number 1 of rule 'pdflatex'
> ------------
> ------------
> Running 'pdflatex --synctex=1 --file-line-error -recorder "topologybook.tex"'
> ------------
> Latexmk: applying rule 'pdflatex'...
> This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017) (preloaded format=pdflatex)
> restricted \write18 enabled.
> entering extended mode
> (./topologybook.tex
> LaTeX2e <2017-04-15>
> Babel <3.12> and hyphenation patterns for 84 language(s) loaded.
> (/usr/local/texlive/2017/texmf-dist/tex/latex/snapshot/snapshot.sty)
> (/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/memoir.cls
> Document Class: memoir 2016/05/16 v3.7f configurable book, report, article docu
> ment class
> (/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ifpdf.sty)
> (/usr/local/texlive/2017/texmf-dist/tex/latex/ifetex/ifetex.sty
> (/usr/local/texlive/2017/texmf-dist/tex/plain/ifetex/ifetex.tex))
> (/usr/local/texlive/2017/texmf-dist/tex/generic/ifxetex/ifxetex.sty)
> (/usr/local/texlive/2017/texmf-dist/tex/generic/oberdiek/ifluatex.sty)
> (/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/mem10.clo)
> (/usr/local/texlive/2017/texmf-dist/tex/latex/memoir/mempatch.sty))
> (/usr/local/texlive/2017/texmf-dist/tex/latex/base/ifthen.sty)
> (./preamble/preamble.tex (./preamble/packages.sty
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> (/usr/local/texlive/2017/texmf-dist/tex/latex/etoolbox/etoolbox.sty)
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> (/usr/local/texlive/2017/texmf-dist/tex/latex/csquotes/csquotes.def)
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> (/usr/local/texlive/2017/texmf-dist/tex/latex/amsmath/amsmath.sty
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> (/usr/local/texlive/2017/texmf-dist/tex/latex/amsmath/amstext.sty
> (/usr/local/texlive/2017/texmf-dist/tex/latex/amsmath/amsgen.sty))
> (/usr/local/texlive/2017/texmf-dist/tex/latex/amsmath/amsbsy.sty)
> (/usr/local/texlive/2017/texmf-dist/tex/latex/amsmath/amsopn.sty))
> (/usr/local/texlive/2017/texmf-dist/tex/latex/amscls/amsthm.sty)
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> nput line 1165.
>
> ) (./main/SetsMaps/families.tex
>
> Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
> (hyperref) removing `math shift' on input line 48.
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> LaTeX Warning: Reference `subsec:union-intersect-two' on page 1 undefined on in
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> 399.
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> LaTeX Warning: Reference `subsec:ordered-pairs' on page 1 undefined on input li
> ne 564.
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> ne 564.
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> LaTeX Warning: Reference `subsec:composite' on page 1 undefined on input line 5
> 82.
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> LaTeX Warning: Reference `def:power-of-set' on page 1 undefined on input line 6
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> line 859.
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> n input line 900.
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> [44]
> Overfull \hbox (2.57535pt too wide) in paragraph at lines 909--910
> []\T1/hlh/m/n/10 (-20) Let $\OML/hlcm/m/it/10 n$ \T1/hlh/m/n/10 (-20) be a pos-
> i-tive in-te-ger and let $\OML/hlcm/m/it/10 ÑX[]Ö[]$ \T1/hlh/m/n/10 (-20) be a
> fam-ily of \T1/hlh/m/it/10 (-20) nonempty
>
> LaTeX Warning: Reference `cor:section-and-retraction-implies-inj-surj' on page
> 1 undefined on input line 938.
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>
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> fined on input line 938.
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>
> ) (./main/SetsMaps/recursion.tex [45] [46]
>
> LaTeX Warning: Reference `prop-eq:IC-and-recurrence' on page 47 undefined on in
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>
>
> LaTeX Warning: Reference `pf-eq:recurse-2' on page 47 undefined on input line 1
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> LaTeX Warning: Reference `prop:extend-many-pieces' on page 1 undefined on input
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>
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> [47]
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> 83.
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> [49]
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> LaTeX Warning: Reference `cor-eq-primitive-recurse' on page 50 undefined on inp
> ut line 320.
>
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>
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> LaTeX Warning: Reference `thm:ordinary-recursion' on page 50 undefined on input
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>
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>
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> LaTeX Warning: Reference `pf-eq-primitive-recurse-1' on page 51 undefined on in
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>
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>
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> ut line 403.
>
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>
>
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> t line 413.
>
>
> LaTeX Warning: Reference `thm:complete-recursion' on page 51 undefined on input
> line 441.
>
>
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> input line 441.
>
> [51]
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> LaTeX Warning: Reference `def:union-intersection-family' on page 1 undefined on
> input line 520.
>
> [52]
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>
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> LaTeX Warning: Reference `cor:primitive-recursion' on page 1 undefined on input
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>
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> LaTeX Warning: Reference `thm:complete-recursion' on page 53 undefined on input
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>
>
> LaTeX Warning: Reference `thm:complete-recursion' on page 53 undefined on input
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>
> ) (./main/SetsMaps/countable.tex
>
> LaTeX Warning: Reference `def:one-one-corr' on page 1 undefined on input line 1
> 0.
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> [53]
> Overfull \hbox (3.3389pt too wide) in paragraph at lines 84--88
> \T1/hlh/m/n/10 (-20) Hence the map ob-tained from $\OML/hlcm/m/it/10 h[]$ \T1/h
> lh/m/n/10 (-20) by re-strict-ing its do-main to $\OMS/hlcy/m/n/10 f\T1/hlh/m/n/
> 10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ; n;
> n \OMS/hlcy/m/n/10 Ç
>
> LaTeX Warning: Reference `prop:union-finite-family-of-finite-sets' on page 1 un
> defined on input line 99.
>
> [54]
> Overfull \hbox (10.72176pt too wide) in paragraph at lines 152--155
> []\T1/hlh/m/n/10 (-20) Now let $\OML/hlcm/m/it/10 n \OMS/hlcy/m/n/10 ^^U \T1/hl
> h/m/n/10 (-20) 1$ and as-sume that each sub-set of $\OMS/hlcy/m/n/10 f\T1/hlh/m
> /n/10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ;
> n\OMS/hlcy/m/n/10 g$
>
> LaTeX Warning: Reference `lem:disj-union-finite-sets' on page 1 undefined on in
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>
>
> LaTeX Warning: Reference `ex:N-is-infinite' on page 1 undefined on input line 1
> 71.
>
> [55]
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> LaTeX Warning: Reference `prop:subset-of-finite' on page 1 undefined on input l
> ine 191.
>
>
> LaTeX Warning: Reference `lem:disj-union-finite-sets' on page 1 undefined on in
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>
>
> LaTeX Warning: Reference `prop:union-finite-family-of-finite-sets' on page 1 un
> defined on input line 240.
>
>
> LaTeX Warning: Reference `prop:union-finite-family-of-finite-sets' on page 1 un
> defined on input line 243.
>
> [56]
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> LaTeX Warning: Reference `thm:wo-principle' on page 57 undefined on input line
> 258.
>
>
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> 258.
>
>
> LaTeX Warning: Reference `prop:subset-of-finite' on page 1 undefined on input l
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> [57]
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> LaTeX Warning: Reference `prop:subset-of-finite' on page 1 undefined on input l
> ine 345.
>
>
> LaTeX Warning: Reference `prop:inf-subset-of-countable' on page 1 undefined on
> input line 372.
>
>
> LaTeX Warning: Reference `ex:N-is-infinite' on page 1 undefined on input line 3
> 74.
>
>
> LaTeX Warning: Reference `prop:subset-of-finite' on page 1 undefined on input l
> ine 374.
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> LaTeX Warning: Reference `thm:complete-recursion' on page 59 undefined on input
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>
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> LaTeX Warning: Reference `thm:complete-recursion' on page 59 undefined on input
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>
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> LaTeX Warning: Reference `cor:AC-choice-function' on page 1 undefined on input
> line 394.
>
>
> LaTeX Warning: Reference `prop:image-of-finite-set' on page 1 undefined on inpu
> t line 406.
>
>
> LaTeX Warning: Reference `prop:image-of-countable-set' on page 1 undefined on i
> nput line 417.
>
>
> LaTeX Warning: Reference `pf-eq:two-three-powers' on page 59 undefined on input
> line 448.
>
> [59]
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> nput line 485.
>
>
> LaTeX Warning: Reference `lem:N-times-N-denumerable' on page 1 undefined on inp
> ut line 485.
>
>
> LaTeX Warning: Reference `thm:countable-union-of-countable-sets' on page 1 unde
> fined on input line 491.
>
>
> LaTeX Warning: Reference `prob:Z-is-denumerable' on page 1 undefined on input l
> ine 496.
>
>
> LaTeX Warning: Reference `cor:product-finite-family-countable-sets' on page 1 u
> ndefined on input line 519.
>
> [60] [61]
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> LaTeX Warning: Reference `ex:uncountable-product-of-doubletons' on page 1 undef
> ined on input line 586.
>
>
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> [62]
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>
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>
>
> LaTeX Warning: Reference `cor:AC-choice-function' on page 1 undefined on input
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>
> ) (./main/SetsMaps/ordering.tex
>
> LaTeX Warning: Reference `def:antisymmetric' on page 64 undefined on input line
> 66.
>
>
> LaTeX Warning: Reference `def:partial-order' on page 1 undefined on input line
> 66.
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> LaTeX Warning: Reference `def:comparable' on page 64 undefined on input line 66
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> LaTeX Warning: Reference `def:comparable' on page 1 undefined on input line 66.
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> LaTeX Warning: Reference `cref' on page 67 undefined on input line 292.
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>
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> ine 292.
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>
>
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> 398.
>
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>
> [69] [70]
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> LaTeX Warning: Reference `thm:intervals-in-R' on page 1 undefined on input line
> 552.
>
> [71] [72] [73]
>
> LaTeX Warning: Reference `fig:dictionary-order' on page 1 undefined on input li
> ne 733.
>
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> LaTeX Warning: Reference `cref' on page 75 undefined on input line 768.
>
>
> LaTeX Warning: Reference `ex:partial-orders' on page 1 undefined on input line
> 768.
>
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> [75] [76]
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> LaTeX Warning: Reference `def:upper-bound-property-of-direction' on page 77 und
> efined on input line 907.
>
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> e 956.
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>
> LaTeX Warning: Reference `cref' on page 77 undefined on input line 961.
>
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> LaTeX Warning: Reference `ex:partial-orders' on page 1 undefined on input line
> 961.
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> e 961.
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>
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> 966.
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> LaTeX Warning: Reference `prob:preorder-is-generated-like-that' on page 1 undef
> ined on input line 1050.
>
>
> LaTeX Warning: Reference `prob:generate-preorder-from-surj' on page 1 undefined
> on input line 1055.
>
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> LaTeX Warning: Reference `sec:equiv' on page 1 undefined on input line 1056.
>
>
> LaTeX Warning: Reference `prob:generate-preorder-from-surj' on page 1 undefined
> on input line 1086.
>
> ) (./main/SetsMaps/ordercomplete.tex [79]
>
> LaTeX Warning: Reference `ax:R-order-complete' on page 1 undefined on input lin
> e 55.
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> [80] [81]
>
> LaTeX Warning: Reference `thm:closed-interval-R-uncountable' on page 1 undefine
> d on input line 200.
>
>
> LaTeX Warning: Reference `def:interval' on page 1 undefined on input line 214.
>
>
> LaTeX Warning: Reference `txt:std-intervals' on page 1 undefined on input line
> 226.
>
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> LaTeX Warning: Reference `pfcase:all-intervals-lower-not-upper-bound' on page 1
> undefined on input line 275.
>
> ) (./main/SetsMaps/equivrel.tex [83]) (./main/SetsMaps/well-ordering.tex
>
> LaTeX Warning: Reference `def:comparable' on page 84 undefined on input line 19
> .
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> e 100.
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> ne 109.
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> LaTeX Warning: Reference `lem:bded-above-subset-wo-has-sup' on page 1 undefined
> on input line 158.
>
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> input line 167.
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> on input line 180.
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> ne 183.
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> ine 226.
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>
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> ne 230.
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> on input line 240.
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> LaTeX Warning: Reference `thm-wo' on page 1 undefined on input line 319.
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>
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> LaTeX Warning: Citation 'GraysonZorn2007' on page 88 undefined on input line 32
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> LaTeX Warning: Reference `ax:AC' on page 89 undefined on input line 405.
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> LaTeX Warning: Reference `eq:star-zorn-pf' on page 90 undefined on input line 4
> 83.
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> LaTeX Warning: Reference `pf:zorn-step-6' on page 1 undefined on input line 577
> .
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> ine 577.
>
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>
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> Package thmtools Warning: Unused key `refname' on input line 619.
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> []\T1/hlh/m/n/10 (-20) The pre-ced-ing proof is a typ-i-cal pro-ce-dure for ap-
> ply-ing Zorn's Lemma.To
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> []\T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) Continuation of [].\T1/hlh/m/n/10
> (-20) ) Prove the \T1/hlh/b/n/10 Teichm¸ller-Tukey Lemma\T1/hlh/m/n/10 (-20) :
> A nonempty
>
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> )) [95] (./main/MetricSpaces/chapterMetrics.tex [96]
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> LaTeX Warning: Reference `sec:compactmetric' on page 1 undefined on input line
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> [98]
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> []\T1/hlh/m/n/10 (-20) Since $\OML/hlcm/m/it/10 dÑx; yÖ \OMS/hlcy/m/n/10 É k\OM
> L/hlcm/m/it/10 x \OMS/hlcy/m/n/10 ^^@ \OML/hlcm/m/it/10 y\OMS/hlcy/m/n/10 k$\T1
> /hlh/m/n/10 (-20) , then from [] [] we have $\OML/hlcm/m/it/10 dÑx; yÖ \OMS/hlc
> y/m/n/10 É
>
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> []\T1/hls/b/n/10 1.9 Ex-am-ple. []\T1/hlh/m/n/10 (-20) Again let $\OML/hlcm/m/i
> t/10 X$ \T1/hlh/m/n/10 (-20) be the set of all con-tin-u-ous func-tions $\OML/h
> lcm/m/it/10 x [] [] Ü\T1/hlh/m/n/10 (-20) 0\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (
> -20) 1\OML/hlcm/m/it/10 á [] \LMR/hlcm/m/n/10 R$\T1/hlh/m/n/10 (-20) .
>
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> [111] [112]
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> []\T1/hlh/m/n/10 (-20) Are the taxi-cab and max met-rics on $\LMR/hlcm/m/n/10 R
> []$ \T1/hlh/m/n/10 (-20) also translation-invariant?
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>
> LaTeX Warning: Reference `prob:taxicab-equiv-euclidean' on page 1 undefined on
> input line 110.
>
>
> LaTeX Warning: Reference `ex:sup-metric-on-functions' on page 142 undefined on
> input line 123.
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> nput line 123.
>
> [142]
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> 42.
>
>
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> ne 163.
>
> [143]
>
> LaTeX Warning: Reference `prop:bded-metric-equiv-to-given' on page 1 undefined
> on input line 180.
>
>
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> e 198.
>
> [144]
>
> LaTeX Warning: Reference `def:bounded' on page 1 undefined on input line 220.
>
> pdfTeX warning (ext4): destination with the same identifier (name{proposition.3
> 8}) has been already used, duplicate ignored
> <to be read again>
> \relax
> l.250 \label
> {prop:bded-metric-equiv-to-given} [145]
>
> LaTeX Warning: Reference `prop:bded-metric-equiv-to-given' on page 1 undefined
> on input line 292.
>
>
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>
>
> LaTeX Warning: Reference `ex:limits-in-calculus' on page 1 undefined on input l
> ine 294.
>
>
> LaTeX Warning: Reference `ex:limits-at-infty' on page 1 undefined on input line
> 294.
>
>
> LaTeX Warning: Reference `ex:infinite-limits' on page 146 undefined on input li
> ne 294.
>
> [146]
>
> LaTeX Warning: Reference `fig:map-R-to-interval' on page 1 undefined on input l
> ine 342.
>
> [147] [148] [149] [150]
>
> LaTeX Warning: Reference `prob:translation-rotation-invariant-metrics' on page
> 1 undefined on input line 571.
>
> pdfTeX warning (ext4): destination with the same identifier (name{definition.43
> }) has been already used, duplicate ignored
> <to be read again>
> \relax
> l.582 \label
> {def:isometry} [151]pdfTeX warning (ext4): destination with the sam
> e identifier (name{examples.44}) has been already used, duplicate ignored
> <to be read again>
> \relax
> l.610 \label
> {ex:isometries}
>
> LaTeX Warning: Reference `prob:translation-rotation-invariant-metrics' on page
> 1 undefined on input line 635.
>
>
> Overfull \hbox (25.85425pt too wide) detected at line 643
> []
>
> LaTeX Warning: Citation 'JacobBaileyLinearAlgebra' on page 152 undefined on inp
> ut line 648.
>
>
> LaTeX Warning: Citation 'ChrisCooperIsometries' on page 152 undefined on input
> line 648.
>
>
> LaTeX Warning: Citation 'ChrisCooperIsometries3D' on page 152 undefined on inpu
> t line 648.
>
>
> LaTeX Warning: Citation 'FlemingSeveralVars2Ed' on page 152 undefined on input
> line 648.
>
>
> LaTeX Warning: Citation 'KConradIsometries' on page 152 undefined on input line
> 648.
>
>
> LaTeX Warning: Reference `prob:ip-and-isometry' on page 1 undefined on input li
> ne 649.
>
> [152]
>
> LaTeX Warning: Citation 'FlemingSeveralVars2Ed' on page 153 undefined on input
> line 701.
>
>
> LaTeX Warning: Citation 'KConradIsometries' on page 153 undefined on input line
> 701.
>
>
> Overfull \hbox (10.61795pt too wide) detected at line 746
> \OML/hlcm/m/it/10 d[]Ñy[]; y[]Ö \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 d[][]fÑx[]
> Ö; fÑx[]Ö[] \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 dÑx[]; x[]Ö \OMS/hlcy/m/n/10 É
> \OML/hlcm/m/it/10 d[]f[]Ñy[]Ö; f[]Ñy[]Ö[]: []
>
> LaTeX Warning: Reference `prop:isometries-equiv-relation' on page 1 undefined o
> n input line 753.
>
> pdfTeX warning (ext4): destination with the same identifier (name{definition.46
> }) has been already used, duplicate ignored
> <to be read again>
> \relax
> l.765 \label
> {def:top-equiv-metric-spaces} [153]pdfTeX warning (ext4): destinati
> on with the same identifier (name{examples.47}) has been already used, duplicat
> e ignored
> <to be read again>
> \relax
> l.786 \label
> {ex:top-equiv-metric-spaces}
>
> LaTeX Warning: Reference `def:equivalent-metrics' on page 1 undefined on input
> line 793.
>
>
> LaTeX Warning: Reference `ex:equiv-metrics-implies-top-equiv' on page 1 undefin
> ed on input line 797.
>
>
> Overfull \hbox (16.05836pt too wide) in paragraph at lines 831--832
> []\T1/hlh/m/n/10 (-20) The met-ric space $\OML/hlcm/m/it/10 ÑÜ\T1/hlh/m/n/10 (-
> 20) 0\OML/hlcm/m/it/10 ; cá; dÖ$ \T1/hlh/m/n/10 (-20) is topo-log-i-cally equiv
> -a-lent to $\OML/hlcm/m/it/10 ÑÜa; bá; d[]Ö$\T1/hlh/m/n/10 (-20) .
> [154]
> Overfull \hbox (25.11824pt too wide) in paragraph at lines 843--846
> \T1/hlh/m/n/10 (-20) ---the com-pos-ite of a trans-la-tion fol-lowed by a di-la
> -tion or contraction---
>
> LaTeX Warning: Reference `prop:isometries-equiv-relation' on page 1 undefined o
> n input line 862.
>
>
> LaTeX Warning: Reference `prop-part:top-equiv-metric-reflexive' on page 1 undef
> ined on input line 892.
>
>
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>
>
> LaTeX Warning: Reference `ex:top-equiv-metric-spaces' on page 1 undefined on in
> put line 892.
>
>
> LaTeX Warning: Reference `ex:equiv-metrics-implies-top-equiv' on page 1 undefin
> ed on input line 892.
>
>
> LaTeX Warning: Reference `chap:spaces' on page 1 undefined on input line 897.
>
> [155]
>
> LaTeX Warning: Reference `prob:cf-taxicab-euclidean-d' on page 1 undefined on i
> nput line 916.
>
>
> LaTeX Warning: Reference `prob-part:def-metric-on-seq-bded-metric-spaces' on pa
> ge 1 undefined on input line 945.
>
>
> LaTeX Warning: Reference `ex:sequence-space-metric' on page 1 undefined on inpu
> t line 945.
>
>
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> nput line 952.
>
>
> LaTeX Warning: Reference `prob-part:hilbert-cube' on page 1 undefined on input
> line 952.
>
>
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> ut line 953.
>
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> ndefined on input line 985.
>
>
> Overfull \hbox (0.39265pt too wide) in paragraph at lines 993--995
> []\T1/hlh/m/n/10 (-20) Let $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) be the col
> -lec-tion of all nonempty $\OML/hlcm/m/it/10 d$\T1/hlh/m/n/10 (-20) -closed sub
> -sets of a bounded
> [156]
>
> LaTeX Warning: Reference `prob:dist-between-sets' on page 1 undefined on input
> line 1005.
>
>
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> 1 undefined on input line 1018.
>
>
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> ut line 1025.
>
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>
> [157]
>
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> e 1071.
>
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> e 1081.
>
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> e 1081.
>
>
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> 1107.
>
>
> LaTeX Warning: Reference `prob:translation-rotation-invariant-metrics' on page
> 1 undefined on input line 1119.
>
> [158]
>
> LaTeX Warning: Reference `prop-part:top-equiv-metric-symmetric' on page 1 undef
> ined on input line 1158.
>
>
> LaTeX Warning: Reference `prop-part:top-equiv-metric-transitive' on page 1 unde
> fined on input line 1158.
>
>
> LaTeX Warning: Reference `prop:top-equiv-metric-equiv-relation' on page 1 undef
> ined on input line 1158.
>
> ) (./main/MetricSpaces/contconv.tex
>
> LaTeX Warning: Reference `sec:metrics' on page 1 undefined on input line 16.
>
> pdfTeX warning (ext4): destination with the same identifier (name{definition.49
> }) has been already used, duplicate ignored
> <to be read again>
> \relax
> l.20 \label
> {def:cont-metric} [159]pdfTeX warning (ext4): destination with the s
> ame identifier (name{examples.50}) has been already used, duplicate ignored
> <to be read again>
> \relax
> l.51 \label
> {ex:cont-metric}
>
> LaTeX Warning: Reference `def:cont-metric' on page 1 undefined on input line 58
> .
>
>
> Underfull \vbox (badness 1430) has occurred while \output is active [160]
> [161]
>
> LaTeX Warning: Reference `ex:max-metric-on-product' on page 1 undefined on inpu
> t line 163.
>
>
> Overfull \hbox (5.56319pt too wide) in paragraph at lines 181--181
> []
>
> LaTeX Warning: Reference `def:cont-metric' on page 1 undefined on input line 19
> 7.
>
>
> LaTeX Warning: Reference `def:cont-metric' on page 1 undefined on input line 19
> 7.
>
> [162]
> Overfull \hbox (21.48416pt too wide) in paragraph at lines 222--223
> []\T1/hlh/m/it/10 (-20) For each $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/it/10 (-20) -
> neighborhood $\OML/hlcm/m/it/10 N$ \T1/hlh/m/it/10 (-20) of $\OML/hlcm/m/it/10
> fÑxÖ$ \T1/hlh/m/it/10 (-20) in $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/it/10 (-20) ther
> e ex-ists some $\OML/hlcm/m/it/10 d$\T1/hlh/m/it/10 (-20) -neighborhood
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page
> 1 undefined on input line 234.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o
> n page 1 undefined on input line 234.
>
>
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> n page 1 undefined on input line 235.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image
> ' on page 1 undefined on input line 235.
>
>
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> ' on page 1 undefined on input line 236.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page
> 1 undefined on input line 236.
>
>
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> 1 undefined on input line 241.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o
> n page 1 undefined on input line 241.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page
> 1 undefined on input line 242.
>
>
> LaTeX Warning: Reference `fig:pf-1then2-metric-cont-at-pt' on page 1 undefined
> on input line 253.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page
> 1 undefined on input line 253.
>
>
> LaTeX Warning: Reference `fig:pf-1then2-metric-cont-at-pt' on page 1 undefined
> on input line 253.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page
> 1 undefined on input line 253.
>
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 258.
>
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 258.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o
> n page 1 undefined on input line 262.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image
> ' on page 1 undefined on input line 262.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o
> n page 1 undefined on input line 263.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o
> n page 1 undefined on input line 265.
>
> [163]
>
> LaTeX Warning: Reference `fig:pf-2then3-metric-cont-at-pt' on page 1 undefined
> on input line 274.
>
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 278.
>
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 278.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image
> ' on page 1 undefined on input line 287.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-cont' on page
> 1 undefined on input line 287.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image
> ' on page 1 undefined on input line 288.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image
> ' on page 1 undefined on input line 291.
>
>
> Overfull \hbox (1.13252pt too wide) in paragraph at lines 288--293
> []\T1/hlh/m/n/10 (-20) Assume []. Let $\OML/hlcm/m/it/10 " > \T1/hlh/m/n/10 (-2
> 0) 0$. Since $\OML/hlcm/m/it/10 B[]ÑfÑxÖ\T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/1
> 0 d[]Ö$ \T1/hlh/m/n/10 (-20) is a $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/n/10 (-20) -
> neighborhood
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image
> ' on page 1 undefined on input line 312.
>
>
> LaTeX Warning: Reference `prob:metric-open-map-nowhere-cont' on page 1 undefine
> d on input line 326.
>
> [164]
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 334.
>
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 337.
>
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 343.
>
>
> Overfull \hbox (10.55005pt too wide) in paragraph at lines 343--344
> []\T1/hlh/m/n/10 (-20) From [] we may now de-duce an es-pe-cially sim-ple cri-t
> e-rion for continuity---
>
> LaTeX Warning: Reference `prop:d-open-iff-nbd-each-pt' on page 1 undefined on i
> nput line 367.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-inverse-image
> ' on page 165 undefined on input line 369.
>
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 370.
>
>
> LaTeX Warning: Reference `thm-property:metric-cont-at-pt-via-nbds-exists-nbd' o
> n page 165 undefined on input line 373.
>
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 373.
>
>
> LaTeX Warning: Reference `thm:continuity-in-metric-via-open-sets' on page 1 und
> efined on input line 391.
>
> [165]
>
> LaTeX Warning: Reference `chap:contconv' on page 1 undefined on input line 400.
>
>
>
> LaTeX Warning: Reference `thm:R-archimedean' on page 1 undefined on input line
> 450.
>
> [166]
>
> LaTeX Warning: Reference `ineq:dxnx-less-than-1' on page 167 undefined on input
> line 514.
>
>
> LaTeX Warning: Reference `ineq:dxnx-less-than-1' on page 167 undefined on input
> line 514.
>
> pdfTeX warning (ext4): destination with the same identifier (name{examples.59})
> has been already used, duplicate ignored
> <to be read again>
> \relax
> l.527 \label
> {ex:seq-conv-metric} [167]
>
> LaTeX Warning: Reference `def:upper-lower-bounds' on page 1 undefined on input
> line 541.
>
>
> LaTeX Warning: Reference `prop:conv-seq-bded' on page 1 undefined on input line
> 547.
>
>
> Overfull \hbox (1.81577pt too wide) in paragraph at lines 547--548
> []\T1/hlh/m/n/10 (-20) In fact, in view of [], the range $\OMS/hlcy/m/n/10 f []
> g$ \T1/hlh/m/n/10 (-20) will cer-tainly be bounded
>
> LaTeX Warning: Reference `ex:increasing-seq-R-bded-above-converges' on page 1 u
> ndefined on input line 568.
>
>
> LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp
> ut line 568.
>
>
> LaTeX Warning: Reference `page-comment:sum-sqs-ell2-bded-above-converges' on pa
> ge 1 undefined on input line 568.
>
> [168]
>
> LaTeX Warning: Reference `prop:conv-seq-bded' on page 1 undefined on input line
> 598.
>
>
> LaTeX Warning: Reference `ex:conv-in-whole-metric-not-in-subsp' on page 1 undef
> ined on input line 606.
>
>
> LaTeX Warning: Reference `cor:rationals-order-dense-in-reals' on page 1 undefin
> ed on input line 626.
>
> [169]
>
> LaTeX Warning: Reference `ex:sup-metric-on-functions' on page 1 undefined on in
> put line 667.
>
> [170]
>
> LaTeX Warning: Reference `def:seq-conv-metric' on page 1 undefined on input lin
> e 701.
>
>
> LaTeX Warning: Reference `thm:conv-via-nbds-metric' on page 1 undefined on inpu
> t line 723.
>
> [171]
>
> LaTeX Warning: Reference `fig:coordinatewise-conv-seq-R2' on page 1 undefined o
> n input line 748.
>
>
> LaTeX Warning: Reference `fig:coordinatewise-conv-seq-Rk' on page 1 undefined o
> n input line 756.
>
>
> LaTeX Warning: Reference `prop:d-and-dmax-equiv' on page 1 undefined on input l
> ine 791.
>
>
> LaTeX Warning: Reference `cor:conv-seq-invariant-of-equiv-metrics' on page 1 un
> defined on input line 791.
>
> [172]
>
> LaTeX Warning: Reference `ex:seq-conv-Rn-iff-conv-coordinatewise' on page 1 und
> efined on input line 829.
>
>
> LaTeX Warning: Reference `ex:max-metric-on-product' on page 1 undefined on inpu
> t line 829.
>
> [173]
>
> LaTeX Warning: Reference `cor:separate-pts-in-metric' on page 1 undefined on in
> put line 844.
>
>
> Overfull \hbox (9.75574pt too wide) in paragraph at lines 844--847
> []\T1/hlh/m/n/10 (-20) Just sup-pose that $\OML/hlcm/m/it/10 x \LMR/hlcm/m/n/10
> î \OML/hlcm/m/it/10 y$\T1/hlh/m/n/10 (-20) . By [] there are dis-joint $\OML/h
> lcm/m/it/10 d$\T1/hlh/m/n/10 (-20) -neighborhoods
>
> LaTeX Warning: Reference `cref' on page 174 undefined on input line 862.
>
>
> LaTeX Warning: Reference `ex:seq-conv-metric' on page 1 undefined on input line
> 862.
>
>
> LaTeX Warning: Reference `ex:conv-in-whole-metric-not-in-subsp' on page 1 undef
> ined on input line 862.
>
>
> LaTeX Warning: Reference `thm:unique-seq-lim-metric' on page 1 undefined on inp
> ut line 866.
>
>
> Underfull \vbox (badness 1331) has occurred while \output is active [174]
>
> LaTeX Warning: Reference `cond:set-d-closed' on page 1 undefined on input line
> 922.
>
>
> LaTeX Warning: Reference `cond:seq-limit-in-set' on page 1 undefined on input l
> ine 922.
>
>
> LaTeX Warning: Reference `cond:set-d-closed' on page 1 undefined on input line
> 923.
>
>
> LaTeX Warning: Reference `cond:seq-limit-in-set' on page 1 undefined on input l
> ine 928.
>
>
> LaTeX Warning: Reference `cond:set-d-closed' on page 1 undefined on input line
> 928.
>
>
> LaTeX Warning: Reference `cond:seq-limit-in-set' on page 1 undefined on input l
> ine 929.
>
>
> LaTeX Warning: Reference `cond:seq-limit-in-set' on page 1 undefined on input l
> ine 941.
>
> [175]
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 975.
>
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 989.
>
>
> LaTeX Warning: Reference `thm:cont-via-seq-conv-metric' on page 1 undefined on
> input line 1015.
>
> [176]
>
> LaTeX Warning: Reference `ex:extended-reals' on page 1 undefined on input line
> 1038.
>
>
> LaTeX Warning: Reference `lem:balls-at-infinity-in-extended-reals' on page 1 un
> defined on input line 1056.
>
>
> LaTeX Warning: Reference `thm:metric-cont-at-pt-via-nbds' on page 1 undefined o
> n input line 1061.
>
>
> LaTeX Warning: Reference `thm:conv-via-nbds-metric' on page 1 undefined on inpu
> t line 1061.
>
> [177]
>
> LaTeX Warning: Reference `def:cont-metric' on page 1 undefined on input line 10
> 81.
>
>
> Overfull \hbox (10.8464pt too wide) in paragraph at lines 1114--1116
> \T1/hlh/m/n/10 (-20) of ad-di-tion and mul-ti-pli-ca-tion, re-spec-tively, are
> $\OML/hlcm/m/it/10 Ñd[]; dÖ$\T1/hlh/m/n/10 (-20) -continuous.
> [178]
>
> LaTeX Warning: Reference `ex:max-metric-on-product' on page 1 undefined on inpu
> t line 1184.
>
>
> LaTeX Warning: Reference `prob-part:proj-finite-prod-metric-is-cont' on page 1
> undefined on input line 1192.
>
>
> LaTeX Warning: Reference `prob:metric-on-seq-bded-metric-spaces' on page 1 unde
> fined on input line 1192.
>
>
> LaTeX Warning: Reference `ex:hilbert-sequence-space' on page 1 undefined on inp
> ut line 1207.
>
>
> LaTeX Warning: Reference `ex:sequence-space-metric' on page 1 undefined on inpu
> t line 1211.
>
> [179]
>
> LaTeX Warning: Reference `ex:sup-metric-on-functions' on page 1 undefined on in
> put line 1226.
>
>
> LaTeX Warning: Reference `ex:L1-metric-on-functions' on page 1 undefined on inp
> ut line 1227.
>
>
> LaTeX Warning: Reference `prob:euclidean-ip' on page 1 undefined on input line
> 1252.
>
>
> LaTeX Warning: Reference `prob:euclidean-ip' on page 1 undefined on input line
> 1261.
>
>
> LaTeX Warning: Reference `inlinedef:convex' on page 1 undefined on input line 1
> 280.
>
>
> LaTeX Warning: Reference `prob:inv-im-closed-is-closed-metric' on page 1 undefi
> ned on input line 1285.
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> \T1/hlh/m/n/10 (-20) For ex-am-ple, any isom-e-try from $\OML/hlcm/m/it/10 ÑX;
> dÖ$ \T1/hlh/m/n/10 (-20) and $\OML/hlcm/m/it/10 ÑY; d[]Ö$ \T1/hlh/m/n/10 (-20)
> is $\OML/hlcm/m/it/10 Ñd; d[]Ö$\T1/hlh/m/n/10 (-20) -uniformly
> )) [185] (./main/TopologicalSpaces/chapterTopological.tex [186]
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> []\T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) Note: \T1/hlh/m/n/10 (-20) A reg-
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> \T1/hlh/m/n/10 (-20) De-fine $\OMS/hlcy/m/n/10 B$ \T1/hlh/m/n/10 (-20) to be t
> he col-lec-tion of all such sub-sets $\OML/hlcm/m/it/10 B[]x[]; x[]; [] ; x[] \
> T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[]; [] ; I[][]$
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> \T1/hlh/m/n/10 (-20) of $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) for all pos-s
> i-ble choices of $\OML/hlcm/m/it/10 k$\T1/hlh/m/n/10 (-20) , of $\OML/hlcm/m/it
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> -20) .
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> )) [244] (./main/ContinuityConvergence/chapterContinuityConvergence.tex
> (./main/ContinuityConvergence/continuityconvergence-init.tex)
> (./main/ContinuityConvergence/continuous.tex [245]
>
> LaTeX Warning: Reference `ex:inequiv-metrics-on-fns' on page 1 undefined on inp
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> []\T1/hlh/m/n/10 (-20) Example [] con-cern-ing the set $\OML/hlcm/m/it/10 X$ \T
> 1/hlh/m/n/10 (-20) of all con-tin-u-ous func-tions $\OML/hlcm/m/it/10 x [] [] Ü
> \T1/hlh/m/n/10 (-20) 0\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 1\OML/hlcm/m/it/
> 10 á [] \LMR/hlcm/m/n/10 R$
>
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> \T1/hlh/m/n/10 (-20) map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/10 S\OML/
> hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$ \T1/hlh/m/n/10 (-2
> 0) is also con-tin-u-ous as a map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/
> 10 T\OML/hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$\T1/hlh/m/
> n/10 (-20) .
>
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> (./main/ContinuityConvergence/productspace.tex
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> ) (./main/ContinuityConvergence/quotientspace.tex [249])
> (./main/ContinuityConvergence/convergence.tex
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>
> LaTeX Warning: Reference `ex:extended-reals' on page 1 undefined on input line
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> )) [251] (./main/Compact/chapterCompact.tex [252]
> (./main/Compact/compact-init.tex) (./main/Compact/compact.tex
> Underfull \vbox (badness 10000) has occurred while \output is active [253]
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> [262]
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> the same identifier (name{corollary.21}) has been already used, duplicate igno
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> th the same identifier (name{corollary.22}) has been already used, duplicate ig
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> 853.
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> 24.
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> Overfull \hbox (6.73897pt too wide) in paragraph at lines 1010--1012
> \T1/hlh/m/n/10 (-20) log-i-cal space $\OML/hlcm/m/it/10 X$ \T1/hlh/m/n/10 (-20)
> to a com-pact space $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/n/10 (-20) whose graph $[]
> $
>
> LaTeX Warning: Reference `thm:cpt-via-nets' on page 1 undefined on input line 1
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> Overfull \hbox (8.11954pt too wide) in paragraph at lines 1013--1015
> []$ \T1/hlh/m/n/10 (-20) con-verges to $\OML/hlcm/m/it/10 fÑxÖ$ \T1/hlh/m/n/10
> (-20) in $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/n/10 (-20) by ap-ply-ing [] to $[]$.
> ) (./main/Compact/compactmetric.tex [269]
>
> LaTeX Warning: Reference `thm:cpt-metrizable-implies-2nd-countable' on page 1 u
> ndefined on input line 47.
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> ndefined on input line 54.
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> undefined on input line 64.
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> input line 67.
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> ion.36}) has been already used, duplicate ignored
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> t line 120.
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> ned on input line 382.
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> tifier (name{corollary.43}) has been already used, duplicate ignored
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> .
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> Overfull \hbox (49.65659pt too wide) in paragraph at lines 660--662
> []\T1/hlh/m/n/10 (-20) [\T1/hlh/m/it/10 (-20) Hint: \T1/hlh/m/n/10 (-20) Form t
> he col-lec-tion $\OMS/hlcy/m/n/10 f [] g$ \T1/hlh/m/n/10 (-20) where $\OML/hlcm
> /m/it/10 E[] \OMS/hlcy/m/n/10 É f [] g$
> ) (./main/Compact/locallycompact.tex [278])) [279]
> (./main/Connected/chapterConnected.tex [280]
> (./main/Connected/connected-init.tex) (./main/Connected/connected.texpdfTeX war
> ning (ext4): destination with the same identifier (name{definition.1}) has been
> already used, duplicate ignored
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> ith the same identifier (name{examples.9}) has been already used, duplicate ign
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>
> [284]) (./main/Connected/pathconnected.tex) (./main/Connected/homotopy.tex)
> (./main/Connected/simplyconnected.tex [285])) [286]
> (./main/Embedding/chapterEmbedding.tex (./main/Embedding/separation.tex)
> (./main/Embedding/metrization.texpdfTeX warning (ext4): destination with the sa
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> orem.2}) has been already used, duplicate ignored
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> [287])) [288])
> (./back/backmatter.tex (./back/exerciseguide.tex
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> [289] [290]) (./back/indexes.tex
> No file topologybook.nls.
> No file notation.gls.
> No file names.ind.
> No file topologybook.ind.
> )) (./topologybook.aux
> No file front/frontmatter.aux.
> No file front/preface.aux.
> (./main/SetsMaps/chapterSetsMaps.aux) (./main/MetricSpaces/chapterMetrics.aux)
> (./main/TopologicalSpaces/chapterTopological.aux)
> (./main/ContinuityConvergence/chapterContinuityConvergence.aux)
> (./main/Compact/chapterCompact.aux) (./main/Connected/chapterConnected.aux)
> (./main/Embedding/chapterEmbedding.aux) (./back/backmatter.aux))
> Dependency list written on topologybook.dep.
>
> Package rerunfilecheck Warning: File `topologybook.out' has changed.
> (rerunfilecheck) Rerun to get outlines right
> (rerunfilecheck) or use package `bookmark'.
>
>
> LaTeX Warning: There were undefined references.
>
>
> LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.
>
>
> Package biblatex Warning: Please (re)run BibTeX on the file(s):
> (biblatex) topologybook
> (biblatex) and rerun LaTeX afterwards.
>
> )
> (see the transcript file for additional information){/usr/local/texlive/2017/te
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> h/lucida/lbd.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbdi.pfb></
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> usr/local/texlive/2017/texmf-dist/fonts/type1/public/xypic/xybtip10.pfb>
> Output written on topologybook.pdf (294 pages, 1069203 bytes).
> SyncTeX written on topologybook.synctex.gz.
> Transcript written on topologybook.log.
> Latexmk: Index file 'notation.idx' was written
> Latexmk: Index file 'names.idx' was written
> Latexmk: Index file 'topologybook.idx' was written
> Latexmk: Non-existent bbl file 'topologybook.bbl'
> No file topologybook.bbl.
> ===========Latexmk: Missing input file: 'topologybook.nls' from line
> 'No file topologybook.nls.'
> Latexmk: Missing input file: 'topologybook.nls' from line
> 'No file topologybook.nls.'
> ===========Latexmk: Missing input file: 'notation.gls' from line
> 'No file notation.gls.'
> Latexmk: Missing input file: 'notation.gls' from line
> 'No file notation.gls.'
> ===========Latexmk: Missing input file: 'names.ind' from line
> 'No file names.ind.'
> Latexmk: Missing input file: 'names.ind' from line
> 'No file names.ind.'
> ===========Latexmk: Missing input file: 'topologybook.ind' from line
> 'No file topologybook.ind.'
> Latexmk: Missing input file: 'topologybook.ind' from line
> 'No file topologybook.ind.'
> ===========Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> ===========Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> Latexmk: Log file says output to 'topologybook.pdf'
> Latexmk: Couldn't find aux file 'front/frontmatter.aux'
> Latexmk: Couldn't find aux file 'front/preface.aux'
> === TeX engine is 'pdfTeX'
> Latexmk: Found bibliography file(s) [mytopologybook.bib mytopologyread.bib topologybook-blx.bib]
> Latexmk: Summary of warnings:
> Latex failed to resolve 1135 reference(s)
> Latex failed to resolve 19 citation(s)
> Rule 'cusdep nlo nls topologybook': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'topologybook.nlo'
> Non-existent destination files:
> 'topologybook.nls'
> ------------
> Run number 1 of rule 'cusdep nlo nls topologybook'
> ------------
> === Creating rule for 'cusdep nlo nls topologybook'
> Latexmk: applying rule 'cusdep nlo nls topologybook'...
> For rule 'cusdep nlo nls topologybook', running '&do_cusdep( makenlo2nls )' ...
> This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).
> Scanning style file /usr/local/texlive/2017/texmf-dist/makeindex/nomencl/nomencl.ist..........done (10 attributes redefined, 3 ignored).
> Scanning input file topologybook.nlo....done (140 entries accepted, 0 rejected).
> Sorting entries....done (990 comparisons).
> Generating output file topologybook.nls....done (293 lines written, 0 warnings).
> Output written in topologybook.nls.
> Transcript written in topologybook.ilg.
> Rule 'makeindex topologybook.idx': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'topologybook.idx'
> Non-existent destination files:
> 'topologybook.ind'
> ------------
> Run number 1 of rule 'makeindex topologybook.idx'
> ------------
> ------------
> Running 'makeindex -s "topologybook".ist -o "topologybook.ind" "topologybook.idx"'
> ------------
> Latexmk: applying rule 'makeindex topologybook.idx'...
> This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).
> Scanning style file ./topologybook.ist......done (6 attributes redefined, 0 ignored).
> Scanning input file topologybook.idx.....done (1105 entries accepted, 3 rejected).
> Sorting entries...........done (11822 comparisons).
> Generating output file topologybook.ind.....done (949 lines written, 147 warnings).
> Output written in topologybook.ind.
> Transcript written in topologybook.ilg.
> Rule 'bibtex topologybook': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'topologybook.aux'
> Non-existent destination files:
> 'topologybook.bbl'
> ------------
> Run number 1 of rule 'bibtex topologybook'
> ------------
> ------------
> Running 'bibtex "topologybook"'
> ------------
> Latexmk: applying rule 'bibtex topologybook'...
> For rule 'bibtex topologybook', running '&run_bibtex( )' ...
> This is BibTeX, Version 0.99d (TeX Live 2017)
> The top-level auxiliary file: topologybook.aux
> The style file: biblatex.bst
> I couldn't open auxiliary file front/frontmatter.aux
> ---line 25 of file topologybook.aux
> : \@input{front/frontmatter.aux
> : }
> I'm skipping whatever remains of this command
> I couldn't open auxiliary file front/preface.aux
> ---line 39 of file topologybook.aux
> : \@input{front/preface.aux
> : }
> I'm skipping whatever remains of this command
> A level-1 auxiliary file: main/SetsMaps/chapterSetsMaps.aux
> A level-1 auxiliary file: main/MetricSpaces/chapterMetrics.aux
> A level-1 auxiliary file: main/TopologicalSpaces/chapterTopological.aux
> A level-1 auxiliary file: main/ContinuityConvergence/chapterContinuityConvergence.aux
> A level-1 auxiliary file: main/Compact/chapterCompact.aux
> A level-1 auxiliary file: main/Connected/chapterConnected.aux
> A level-1 auxiliary file: main/Embedding/chapterEmbedding.aux
> A level-1 auxiliary file: back/backmatter.aux
> Database file #1: topologybook-blx.bib
> Database file #2: mytopologybook.bib
> Database file #3: mytopologyread.bib
> Biblatex version: 3.3
> (There were 2 error messages)
> Latexmk: One or more aux files is missing for bibtex. I'll try
> to get (pdf)latex to remake them.
> Rule 'makeindex notation.idx': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'notation.idx'
> Non-existent destination files:
> 'notation.ind'
> ------------
> Run number 1 of rule 'makeindex notation.idx'
> ------------
> ------------
> Running 'makeindex -s "topologybook".ist -o "notation.ind" "notation.idx"'
> ------------
> Latexmk: applying rule 'makeindex notation.idx'...
> This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).
> Scanning style file ./topologybook.ist......done (6 attributes redefined, 0 ignored).
> Scanning input file notation.idx...done (0 entries accepted, 0 rejected).
> Nothing written in notation.ind.
> Transcript written in notation.ilg.
> Rule 'makeindex names.idx': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'names.idx'
> Non-existent destination files:
> 'names.ind'
> ------------
> Run number 1 of rule 'makeindex names.idx'
> ------------
> ------------
> Running 'makeindex -s "topologybook".ist -o "names.ind" "names.idx"'
> ------------
> Latexmk: applying rule 'makeindex names.idx'...
> This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).
> Scanning style file ./topologybook.ist......done (6 attributes redefined, 0 ignored).
> Scanning input file names.idx....done (44 entries accepted, 0 rejected).
> Sorting entries....done (249 comparisons).
> Generating output file names.ind....done (100 lines written, 0 warnings).
> Output written in names.ind.
> Transcript written in names.ilg.
> Rule 'pdflatex': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'TopologyEd2metadata.xmpi'
> 'back/backmatter.aux'
> 'main/Compact/chapterCompact.aux'
> 'main/Connected/chapterConnected.aux'
> 'main/ContinuityConvergence/chapterContinuityConvergence.aux'
> 'main/Embedding/chapterEmbedding.aux'
> 'main/MetricSpaces/chapterMetrics.aux'
> 'main/SetsMaps/chapterSetsMaps.aux'
> 'main/TopologicalSpaces/chapterTopological.aux'
> 'names.ind'
> 'notation.ind'
> 'topologybook.aux'
> 'topologybook.bbl'
> 'topologybook.ind'
> 'topologybook.nls'
> 'topologybook.out'
> ------------
> Run number 2 of rule 'pdflatex'
> ------------
> ------------
> Running 'pdflatex --synctex=1 --file-line-error -recorder "topologybook.tex"'
> ------------
> Latexmk: applying rule 'pdflatex'...
> This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017) (preloaded format=pdflatex)
> restricted \write18 enabled.
> entering extended mode
> (./topologybook.tex
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> (./main/mainmatter.tex (./main/SetsMaps/chapterSetsMaps.tex
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> \T1/hlh/m/n/10 (-20) verse re-la-tion $[]$ is \T1/hlh/m/it/10 (-20) not \T1/hlh
> /m/n/10 (-20) func-tional be-cause the set $\OMS/hlcy/m/n/10 f [] g$
> [13] [14]) (./main/SetsMaps/maps.tex [15] [16] [17] [18] [19] [20] [21]
> [22] [23] [24] [25] [26] [27] [28]
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> []\T1/hlh/m/n/10 (-20) In examples ([][]*[][]) of the subsection ``Injections,
> surjections, and bijections''
> [29] [30] [31]) (./main/SetsMaps/families.tex
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> \T1/hlh/m/n/10 (-20) Moreover, the for-mu-las in-volv-ing union and in-ter-sec-
> tion in sub-sec-tion ``Union
> [37] [38] [39] [40] [41] [42] [43] [44]
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> []\T1/hlh/m/n/10 (-20) Let $\OML/hlcm/m/it/10 n$ \T1/hlh/m/n/10 (-20) be a pos-
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> fam-ily of \T1/hlh/m/it/10 (-20) nonempty
> [45]) (./main/SetsMaps/recursion.tex [46] [47] [48] [49] [50] [51] [52])
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> \T1/hlh/m/n/10 (-20) Hence the map ob-tained from $\OML/hlcm/m/it/10 h[]$ \T1/h
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> n \OMS/hlcy/m/n/10 Ç
> [54]
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> []\T1/hlh/m/n/10 (-20) Now let $\OML/hlcm/m/it/10 n \OMS/hlcy/m/n/10 ^^U \T1/hl
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> n\OMS/hlcy/m/n/10 g$
> [55] [56] [57] [58] [59] [60] [61] [62] [63]) (./main/SetsMaps/ordering.tex
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> [86] [87] [88]
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> []\T1/hls/b/n/10 1.9 Ex-am-ple. []\T1/hlh/m/n/10 (-20) Again let $\OML/hlcm/m/i
> t/10 X$ \T1/hlh/m/n/10 (-20) be the set of all con-tin-u-ous func-tions $\OML/h
> lcm/m/it/10 x [] [] Ü\T1/hlh/m/n/10 (-20) 0\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (
> -20) 1\OML/hlcm/m/it/10 á [] \LMR/hlcm/m/n/10 R$\T1/hlh/m/n/10 (-20) .
> [108] [109] [110] [111] [112] [113] [114]
> Overfull \hbox (1.90543pt too wide) in paragraph at lines 1092--1093
> []\T1/hlh/m/n/10 (-20) Are the taxi-cab and max met-rics on $\LMR/hlcm/m/n/10 R
> []$ \T1/hlh/m/n/10 (-20) also translation-invariant?
> [115] [116] [117] [118]) (./main/MetricSpaces/openclosed.tex [119] [120]
> [121] [122] [123] [124] [125] [126] [127] [128] [129] [130]
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> l.864 \label
> {cor:separate-pts-in-metric} [135] [136] [137] [138] [139] [140])
> (./main/MetricSpaces/equivalent.texpdfTeX warning (ext4): destination with the
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> l.250 \label
> {prop:bded-metric-equiv-to-given} [145] [146] [147] [148] [149]
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> Overfull \hbox (25.85425pt too wide) detected at line 643
> []
> [152]
> Overfull \hbox (10.61795pt too wide) detected at line 746
> \OML/hlcm/m/it/10 d[]Ñy[]; y[]Ö \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 d[][]fÑx[]
> Ö; fÑx[]Ö[] \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 dÑx[]; x[]Ö \OMS/hlcy/m/n/10 É
> \OML/hlcm/m/it/10 d[]f[]Ñy[]Ö; f[]Ñy[]Ö[]: []
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> Overfull \hbox (16.05836pt too wide) in paragraph at lines 831--832
> []\T1/hlh/m/n/10 (-20) The met-ric space $\OML/hlcm/m/it/10 ÑÜ\T1/hlh/m/n/10 (-
> 20) 0\OML/hlcm/m/it/10 ; cá; dÖ$ \T1/hlh/m/n/10 (-20) is topo-log-i-cally equiv
> -a-lent to $\OML/hlcm/m/it/10 ÑÜa; bá; d[]Ö$\T1/hlh/m/n/10 (-20) .
>
> Overfull \hbox (25.11824pt too wide) in paragraph at lines 843--846
> \T1/hlh/m/n/10 (-20) ---the com-pos-ite of a trans-la-tion fol-lowed by a di-la
> -tion or contraction---
> [155] [156]
> Overfull \hbox (0.39265pt too wide) in paragraph at lines 993--995
> []\T1/hlh/m/n/10 (-20) Let $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) be the col
> -lec-tion of all nonempty $\OML/hlcm/m/it/10 d$\T1/hlh/m/n/10 (-20) -closed sub
> -sets of a bounded
> [157] [158]) (./main/MetricSpaces/contconv.texpdfTeX warning (ext4): destinatio
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> []\T1/hlh/m/it/10 (-20) For each $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/it/10 (-20) -
> neighborhood $\OML/hlcm/m/it/10 N$ \T1/hlh/m/it/10 (-20) of $\OML/hlcm/m/it/10
> fÑxÖ$ \T1/hlh/m/it/10 (-20) in $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/it/10 (-20) ther
> e ex-ists some $\OML/hlcm/m/it/10 d$\T1/hlh/m/it/10 (-20) -neighborhood
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> []\T1/hlh/m/n/10 (-20) Assume ([][]3[][]). Let $\OML/hlcm/m/it/10 " > \T1/hlh/m
> /n/10 (-20) 0$. Since $\OML/hlcm/m/it/10 B[]ÑfÑxÖ\T1/hlh/m/n/10 (-20) ; \OML/hl
> cm/m/it/10 d[]Ö$ \T1/hlh/m/n/10 (-20) is a $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/n/1
> 0 (-20) -neighborhood
> [164] [165] [166] [167]pdfTeX warning (ext4): destination with the same identif
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> \T1/hlh/m/n/10 (-20) of ad-di-tion and mul-ti-pli-ca-tion, re-spec-tively, are
> $\OML/hlcm/m/it/10 Ñd[]; dÖ$\T1/hlh/m/n/10 (-20) -continuous.
> [178] [179] [180] [181] [182]) (./main/MetricSpaces/complete.tex [183] [184]
> [185]
> Overfull \hbox (2.25098pt too wide) in paragraph at lines 197--199
> \T1/hlh/m/n/10 (-20) For ex-am-ple, any isom-e-try from $\OML/hlcm/m/it/10 ÑX;
> dÖ$ \T1/hlh/m/n/10 (-20) and $\OML/hlcm/m/it/10 ÑY; d[]Ö$ \T1/hlh/m/n/10 (-20)
> is $\OML/hlcm/m/it/10 Ñd; d[]Ö$\T1/hlh/m/n/10 (-20) -uniformly
> )) [186] (./main/TopologicalSpaces/chapterTopological.tex
> (./main/TopologicalSpaces/topological-init.tex)
> (./main/TopologicalSpaces/topologies.tex
> Underfull \vbox (badness 5954) has occurred while \output is active [187]pdfTeX
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> {def:topological-space} [188] [189] [190] [191] [192] [193] [194]pdf
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> []\T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) Note: \T1/hlh/m/n/10 (-20) A reg-
> u-lar space, even a reg-u-lar $\OML/hlcm/m/it/10 T[]$\T1/hlh/m/n/10 (-20) -spac
> e, need not be metrizable---
> [210]) (./main/TopologicalSpaces/boundary.tex [211] [212] [213] [214]pdfTeX war
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> or every subset $A$ of a topological space $X$: [221] [222]pdfTeX warnin
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> LaTeX Warning: Reference `cref' on page 226 undefined on input line 1201.
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> LaTeX Warning: Reference `ex:right-interval-topology-R' on page 1 undefined on
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> LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 650.
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> [236]
> Overfull \hbox (15.12009pt too wide) in paragraph at lines 676--701
> \T1/hlh/m/n/10 (-20) de-picts three mem-bers of a set of the form $\OML/hlcm/m/
> it/10 B[]x[]; x[]; x[]; x[] \T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[];
> I[]; I[][]$\T1/hlh/m/n/10 (-20) .]
>
> Overfull \hbox (39.92242pt too wide) in paragraph at lines 676--701
> \T1/hlh/m/n/10 (-20) De-fine $\OMS/hlcy/m/n/10 B$ \T1/hlh/m/n/10 (-20) to be t
> he col-lec-tion of all such sub-sets $\OML/hlcm/m/it/10 B[]x[]; x[]; [] ; x[] \
> T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[]; [] ; I[][]$
>
> Overfull \hbox (15.45676pt too wide) in paragraph at lines 676--701
> \T1/hlh/m/n/10 (-20) of $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) for all pos-s
> i-ble choices of $\OML/hlcm/m/it/10 k$\T1/hlh/m/n/10 (-20) , of $\OML/hlcm/m/it
> /10 Ñ[]Ö$\T1/hlh/m/n/10 (-20) , and of $\OML/hlcm/m/it/10 Ñ[]Ö$\T1/hlh/m/n/10 (
> -20) .
> [237]
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> [243] [244] [245])) [246]
> (./main/ContinuityConvergence/chapterContinuityConvergence.tex
> (./main/ContinuityConvergence/continuityconvergence-init.tex)
> (./main/ContinuityConvergence/continuous.tex [247]
> Overfull \hbox (13.0625pt too wide) in paragraph at lines 56--59
> \T1/hlh/m/n/10 (-20) map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/10 S\OML/
> hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$ \T1/hlh/m/n/10 (-2
> 0) is also con-tin-u-ous as a map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/
> 10 T\OML/hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$\T1/hlh/m/
> n/10 (-20) .
> ) (./main/ContinuityConvergence/homeomorphism.tex [248])
> (./main/ContinuityConvergence/productspace.tex [249] [250]
>
> LaTeX Warning: Reference `WHAT' on page 1 undefined on input line 128.
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> ) (./main/ContinuityConvergence/quotientspace.tex [251])
> (./main/ContinuityConvergence/convergence.tex
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> \T1/hlh/m/n/10 (-20) log-i-cal space $\OML/hlcm/m/it/10 X$ \T1/hlh/m/n/10 (-20)
> to a com-pact space $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/n/10 (-20) whose graph $[]
> $
> [271]) (./main/Compact/compactmetric.tex [272]pdfTeX warning (ext4): destinatio
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> []\T1/hlh/m/n/10 (-20) [\T1/hlh/m/it/10 (-20) Hint: \T1/hlh/m/n/10 (-20) Form t
> he col-lec-tion $\OMS/hlcy/m/n/10 f [] g$ \T1/hlh/m/n/10 (-20) where $\OML/hlcm
> /m/it/10 E[] \OMS/hlcy/m/n/10 É f [] g$
> ) (./main/Compact/locallycompact.tex)) [281]
> (./main/Connected/chapterConnected.tex [282]
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> [289])) [290])
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> [291] [292]) (./back/indexes.tex (./topologybook.nls [293]
> Underfull \vbox (badness 10000) has occurred while \output is active [294]
> [295])
> No file notation.gls.
> [296] (./names.ind [297] [298]) (./topologybook.ind
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> []\T1/hlh/m/n/10 (-20) Baire Cat-e-gory The-o-rem, [][]184[][], [][]222[][]
>
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> []\T1/hlh/m/n/10 (-20) Bolzano-Weierstrass The-o-rem, [][]276[][]
>
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> []\T1/hlh/m/n/10 (-20) bound (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20) b
> ounded; lower bound;
> [299]
> Overfull \hbox (0.28082pt too wide) in paragraph at lines 95--97
> []\T1/hlh/m/n/10 (-20) co-finite topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/
> m/n/10 (-20) finite-com-
>
> Overfull \hbox (11.63974pt too wide) in paragraph at lines 124--126
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> [300]
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> []| \T1/hlh/m/n/10 (-20) and con-ver-gent se-quence, [][]176[][]
>
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> []| \T1/hlh/m/n/10 (-20) from Eu-clidean $\OML/hlcm/m/it/10 n$\T1/hlh/m/n/10 (-
> 20) -space to real
>
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>
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> []| \T1/hlh/m/it/10 (-20) See also \T1/hlh/m/n/10 (-20) con-nected space; sep-
>
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> \T1/hlh/m/n/10 (-20) a-ra-tion; to-tally dis-con-nected
>
> Overfull \hbox (3.79329pt too wide) in paragraph at lines 215--216
> []\T1/hlh/m/n/10 (-20) distance-preserving map, [][]151[][], [][]152[][]
> [301]
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> []\T1/hlh/m/n/10 (-20) Euclidean in-ner prod-uct, [][]158[][], [][]180[][]
>
> Overfull \hbox (5.04117pt too wide) in paragraph at lines 269--270
> []\T1/hlh/m/n/10 (-20) extreme (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20)
> max-i-mum,minimum)
>
> Overfull \hbox (0.8835pt too wide) in paragraph at lines 282--284
> []\T1/hlh/m/n/10 (-20) first-category set (\T1/hlh/m/it/10 (-20) see \T1/hlh/m
> /n/10 (-20) mea-ger set)
> [302]
> Overfull \hbox (2.30344pt too wide) in paragraph at lines 323--325
> \T1/hlh/m/n/10 (-20) Borel-Lebesgue The-o-rem)
>
> Overfull \hbox (10.56528pt too wide) in paragraph at lines 325--326
> []\T1/hlh/m/n/10 (-20) Heine-Borel-Lebesgue The-o-rem, [][]262[][]
>
> Overfull \hbox (18.59972pt too wide) in paragraph at lines 349--350
> []| \T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) see also \T1/hlh/m/n/10 (-20) e
> l-e-ment,member,subset)
>
> Overfull \hbox (0.43198pt too wide) in paragraph at lines 362--364
> \T1/hlh/m/n/10 (-20) tion,mathematical in-duc-
> [303]
> Overfull \hbox (0.584pt too wide) in paragraph at lines 393--394
> []| \T1/hlh/m/n/10 (-20) of a collection of sets, [][]\T1/hlh/b/it/10 39[][]\T1
> /hlh/m/n/10 (-20) , [][]39[][]--
>
> Overfull \hbox (0.77872pt too wide) in paragraph at lines 469--470
> []| \T1/hlh/m/n/10 (-20) defined piecewise, [][]21[][]--[][]22[][], [][]38[][]-
> -
> [304]
> Overfull \hbox (6.09427pt too wide) in paragraph at lines 495--497
> []| \T1/hlh/m/n/10 (-20) ex-am-ples of, [][]99[][], [][]103[][]--[][]114[][], [
> ][]116[][],
>
> Overfull \hbox (1.06433pt too wide) in paragraph at lines 514--516
> []| \T1/hlh/m/n/10 (-20) topo-log-i-cally equiv-a-lent, [][]\T1/hlh/b/it/10 154
> [][]\T1/hlh/m/n/10 (-20) ,
>
> Overfull \hbox (8.51826pt too wide) in paragraph at lines 516--517
> []\T1/hlh/m/n/10 (-20) metrically equiv-a-lent met-ric spaces,
>
> Overfull \hbox (0.98947pt too wide) in paragraph at lines 543--545
> []\T1/hlh/m/n/10 (-20) neighborhood, [][]\T1/hlh/b/it/10 200[][]\T1/hlh/m/n/10
> (-20) , [][]200[][]--[][]202[][], [][]228[][]
>
> Overfull \hbox (3.06833pt too wide) in paragraph at lines 554--556
> []\T1/hlh/m/n/10 (-20) Niemytzki plane (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/
> 10 (-20) tan-gent disk
> [305]
> Overfull \hbox (9.05663pt too wide) in paragraph at lines 573--574
> []| \T1/hlh/m/n/10 (-20) in second-countable space, [][]272[][]
>
> Overfull \hbox (1.59937pt too wide) in paragraph at lines 591--592
> []| \T1/hlh/m/n/10 (-20) and mul-ti-plica-tive in-verse, [][]20[][]
>
> Overfull \hbox (4.04407pt too wide) in paragraph at lines 599--601
> []\T1/hlh/m/n/10 (-20) order topol-ogy, [][]\T1/hlh/b/it/10 234[][]\T1/hlh/m/n/
> 10 (-20) , [][]234[][]--[][]235[][], [][]244[][]
>
> Overfull \hbox (5.82869pt too wide) in paragraph at lines 608--610
> \T1/hlh/m/n/10 (-20) der-ing; pre-order-ing; strict
>
> Overfull \hbox (20.25978pt too wide) in paragraph at lines 608--610
> \T1/hlh/m/n/10 (-20) weak or-der-ing; well-ordering)
> [306]
> Overfull \hbox (2.26106pt too wide) in paragraph at lines 727--729
> \T1/hlh/m/n/10 (-20) func-tional re-la-tion, or-der
> [307]
> Overfull \hbox (0.88599pt too wide) in paragraph at lines 750--752
> []\T1/hlh/m/n/10 (-20) second-category set (\T1/hlh/m/it/10 (-20) see \T1/hlh/
> m/n/10 (-20) non-mea-
>
> Overfull \hbox (1.03703pt too wide) in paragraph at lines 752--753
> []\T1/hlh/m/n/10 (-20) second-countable space, [][]\T1/hlh/b/it/10 238[][]\T1/h
> lh/m/n/10 (-20) , [][]238[][]
>
> Overfull \hbox (0.32431pt too wide) in paragraph at lines 768--769
> []\T1/hlh/m/n/10 (-20) sequential com-pact-ness, [][]273[][], [][]274[][]
>
> Overfull \hbox (10.40741pt too wide) in paragraph at lines 775--777
> []\T1/hlh/m/n/10 (-20) smaller topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/
> n/10 (-20) coarser topol-
>
> Overfull \hbox (1.25479pt too wide) in paragraph at lines 781--783
> []\T1/hlh/m/n/10 (-20) space (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20) t
> opo-log-i-cal space, met-
>
> Overfull \hbox (6.31657pt too wide) in paragraph at lines 785--786
> []\T1/hlh/m/n/10 (-20) statement (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-2
> 0) pred-i-cate,sentence)
>
> Overfull \hbox (2.04988pt too wide) in paragraph at lines 786--788
> []\T1/hlh/m/n/10 (-20) strict or-der-ing (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/
> n/10 (-20) strict di-rected
>
> Overfull \hbox (2.03561pt too wide) in paragraph at lines 786--788
> \T1/hlh/m/n/10 (-20) or-der-ing; strict par-tial or-
>
> Overfull \hbox (3.09906pt too wide) in paragraph at lines 790--792
> []\T1/hlh/m/n/10 (-20) stronger topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m
> /n/10 (-20) finer topol-
> [308]
> Overfull \hbox (21.70116pt too wide) in paragraph at lines 848--850
> []\T1/hlh/m/n/10 (-20) topologically equiv-a-lent met-ric spaces,
>
> Overfull \hbox (2.37872pt too wide) in paragraph at lines 860--861
> []| \T1/hlh/m/n/10 (-20) gen-er-ated by a col-lec-tion, [][]233[][]
>
> Overfull \hbox (2.37599pt too wide) in paragraph at lines 871--872
> []\T1/hlh/m/n/10 (-20) totally bounded met-ric space, [][]\T1/hlh/b/it/10 270[]
> []
>
> Overfull \hbox (2.131pt too wide) in paragraph at lines 900--901
> []| \T1/hlh/m/n/10 (-20) on com-pact met-ric space, [][]277[][]
> [309]
> Overfull \hbox (0.584pt too wide) in paragraph at lines 906--907
> []| \T1/hlh/m/n/10 (-20) of a collection of sets, [][]\T1/hlh/b/it/10 39[][]\T1
> /hlh/m/n/10 (-20) , [][]39[][]--
>
> Overfull \hbox (8.61229pt too wide) in paragraph at lines 933--935
> []\T1/hlh/m/n/10 (-20) weaker topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n
> /10 (-20) coarser topol-
> [310]))) (./topologybook.aux
> No file front/frontmatter.aux.
> No file front/preface.aux.
> (./main/SetsMaps/chapterSetsMaps.aux) (./main/MetricSpaces/chapterMetrics.aux)
> (./main/TopologicalSpaces/chapterTopological.aux)
> (./main/ContinuityConvergence/chapterContinuityConvergence.aux)
> (./main/Compact/chapterCompact.aux) (./main/Connected/chapterConnected.aux)
> (./main/Embedding/chapterEmbedding.aux) (./back/backmatter.aux))
> Dependency list written on topologybook.dep.
>
> Package rerunfilecheck Warning: File `topologybook.out' has changed.
> (rerunfilecheck) Rerun to get outlines right
> (rerunfilecheck) or use package `bookmark'.
>
>
> LaTeX Warning: There were undefined references.
>
>
> LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.
>
>
> Package biblatex Warning: Please rerun LaTeX.
> (biblatex) Page breaks have changed.
>
> )
> (see the transcript file for additional information)pdfTeX warning (dest): name
> {cite.0 at GoldbergReal1976} has been referenced but does not exist, replaced by a
> fixed one
>
> pdfTeX warning (dest): name{cite.0 at BoasPrimerReal1996} has been referenced but
> does not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at KConradIsometries} has been referenced but d
> oes not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at FlemingSeveralVars2Ed} has been referenced b
> ut does not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at ChrisCooperIsometries3D} has been referenced
> but does not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at ChrisCooperIsometries} has been referenced b
> ut does not exist, replaced by a fixed one
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> pdfTeX warning (dest): name{cite.0 at JacobBaileyLinearAlgebra} has been reference
> d but does not exist, replaced by a fixed one
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> pdfTeX warning (dest): name{cite.0 at GaillardZorn2017} has been referenced but do
> es not exist, replaced by a fixed one
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> pdfTeX warning (dest): name{cite.0 at GraysonZorn2007} has been referenced but doe
> s not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at KneserZorn1950} has been referenced but does
> not exist, replaced by a fixed one
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> pdfTeX warning (dest): name{cite.0 at Suppes1972} has been referenced but does not
> exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at Bernays1991} has been referenced but does no
> t exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at EisenbergSets1971} has been referenced but d
> oes not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at BourbakiSets2004} has been referenced but do
> es not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at PinterSets2014} has been referenced but does
> not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at LakinsMathReasoning2016} has been referenced
> but does not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at EisenbergMathMethod1996} has been referenced
> but does not exist, replaced by a fixed one
>
> {/usr/local/texlive/2017/texmf-dist/fonts/enc/dvips/base/8r.enc}</Users/murray/
> Library/texmf/fonts/type1/bh/lucida/lbd.pfb></Users/murray/Library/texmf/fonts/
> type1/bh/lucida/lbdi.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbi
> .pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbma.pfb></Users/murray
> /Library/texmf/fonts/type1/bh/lucida/lbme.pfb></Users/murray/Library/texmf/font
> s/type1/bh/lucida/lbmo.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/l
> bmr.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbms.pfb></Users/mur
> ray/Library/texmf/fonts/type1/bh/lucida/lbmsd.pfb></Users/murray/Library/texmf/
> fonts/type1/bh/lucida/lbr.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucid
> a/lsd.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lsdi.pfb></Users/m
> urray/Library/texmf/fonts/type1/bh/lucida/lsi.pfb></Users/murray/Library/texmf/
> fonts/type1/bh/lucida/lsr.pfb></usr/local/texlive/2017/texmf-dist/fonts/type1/p
> ublic/xypic/xyatip10.pfb></usr/local/texlive/2017/texmf-dist/fonts/type1/public
> /xypic/xybtip10.pfb>
> Output written on topologybook.pdf (316 pages, 1207459 bytes).
> SyncTeX written on topologybook.synctex.gz.
> Transcript written on topologybook.log.
> Latexmk: Index file 'notation.idx' was written
> Latexmk: Index file 'names.idx' was written
> Latexmk: Index file 'topologybook.idx' was written
> ===========Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> ===========Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> ===========Latexmk: Missing input file: 'notation.gls' from line
> 'No file notation.gls.'
> Latexmk: Missing input file: 'notation.gls' from line
> 'No file notation.gls.'
> ===========Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> ===========Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> Latexmk: Log file says output to 'topologybook.pdf'
> Latexmk: Couldn't find aux file 'front/frontmatter.aux'
> Latexmk: Couldn't find aux file 'front/preface.aux'
> === TeX engine is 'pdfTeX'
> Latexmk: Found bibliography file(s) [mytopologybook.bib mytopologyread.bib topologybook-blx.bib]
> Latexmk: Summary of warnings:
> Latex failed to resolve 9 reference(s)
> Rule 'cusdep nlo nls topologybook': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'topologybook.nlo'
> ------------
> Run number 2 of rule 'cusdep nlo nls topologybook'
> ------------
> Latexmk: applying rule 'cusdep nlo nls topologybook'...
> For rule 'cusdep nlo nls topologybook', running '&do_cusdep( makenlo2nls )' ...
> This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).
> Scanning style file /usr/local/texlive/2017/texmf-dist/makeindex/nomencl/nomencl.ist..........done (10 attributes redefined, 3 ignored).
> Scanning input file topologybook.nlo....done (140 entries accepted, 0 rejected).
> Sorting entries....done (990 comparisons).
> Generating output file topologybook.nls....done (293 lines written, 0 warnings).
> Output written in topologybook.nls.
> Transcript written in topologybook.ilg.
> Rule 'makeindex topologybook.idx': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'topologybook.idx'
> ------------
> Run number 2 of rule 'makeindex topologybook.idx'
> ------------
> ------------
> Running 'makeindex -s "topologybook".ist -o "topologybook.ind" "topologybook.idx"'
> ------------
> Latexmk: applying rule 'makeindex topologybook.idx'...
> This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).
> Scanning style file ./topologybook.ist......done (6 attributes redefined, 0 ignored).
> Scanning input file topologybook.idx.....done (1105 entries accepted, 3 rejected).
> Sorting entries...........done (11818 comparisons).
> Generating output file topologybook.ind.....done (951 lines written, 145 warnings).
> Output written in topologybook.ind.
> Transcript written in topologybook.ilg.
> Rule 'bibtex topologybook': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'back/backmatter.aux'
> 'main/Compact/chapterCompact.aux'
> 'main/Connected/chapterConnected.aux'
> 'main/ContinuityConvergence/chapterContinuityConvergence.aux'
> 'main/Embedding/chapterEmbedding.aux'
> 'main/MetricSpaces/chapterMetrics.aux'
> 'main/SetsMaps/chapterSetsMaps.aux'
> 'main/TopologicalSpaces/chapterTopological.aux'
> 'topologybook.aux'
> ------------
> Run number 2 of rule 'bibtex topologybook'
> ------------
> ------------
> Running 'bibtex "topologybook"'
> ------------
> Latexmk: applying rule 'bibtex topologybook'...
> For rule 'bibtex topologybook', running '&run_bibtex( )' ...
> This is BibTeX, Version 0.99d (TeX Live 2017)
> The top-level auxiliary file: topologybook.aux
> The style file: biblatex.bst
> I couldn't open auxiliary file front/frontmatter.aux
> ---line 25 of file topologybook.aux
> : \@input{front/frontmatter.aux
> : }
> I'm skipping whatever remains of this command
> I couldn't open auxiliary file front/preface.aux
> ---line 39 of file topologybook.aux
> : \@input{front/preface.aux
> : }
> I'm skipping whatever remains of this command
> A level-1 auxiliary file: main/SetsMaps/chapterSetsMaps.aux
> A level-1 auxiliary file: main/MetricSpaces/chapterMetrics.aux
> A level-1 auxiliary file: main/TopologicalSpaces/chapterTopological.aux
> A level-1 auxiliary file: main/ContinuityConvergence/chapterContinuityConvergence.aux
> A level-1 auxiliary file: main/Compact/chapterCompact.aux
> A level-1 auxiliary file: main/Connected/chapterConnected.aux
> A level-1 auxiliary file: main/Embedding/chapterEmbedding.aux
> A level-1 auxiliary file: back/backmatter.aux
> Database file #1: topologybook-blx.bib
> Database file #2: mytopologybook.bib
> Database file #3: mytopologyread.bib
> Biblatex version: 3.3
> (There were 2 error messages)
> Latexmk: One or more aux files is missing for bibtex. I'll try
> to get (pdf)latex to remake them.
> Rule 'makeindex names.idx': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'names.idx'
> ------------
> Run number 2 of rule 'makeindex names.idx'
> ------------
> ------------
> Running 'makeindex -s "topologybook".ist -o "names.ind" "names.idx"'
> ------------
> Latexmk: applying rule 'makeindex names.idx'...
> This is makeindex, version 2.15 [TeX Live 2017] (kpathsea + Thai support).
> Scanning style file ./topologybook.ist......done (6 attributes redefined, 0 ignored).
> Scanning input file names.idx....done (44 entries accepted, 0 rejected).
> Sorting entries....done (249 comparisons).
> Generating output file names.ind....done (100 lines written, 0 warnings).
> Output written in names.ind.
> Transcript written in names.ilg.
> Rule 'pdflatex': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'back/backmatter.aux'
> 'main/Compact/chapterCompact.aux'
> 'main/Connected/chapterConnected.aux'
> 'main/ContinuityConvergence/chapterContinuityConvergence.aux'
> 'main/Embedding/chapterEmbedding.aux'
> 'main/MetricSpaces/chapterMetrics.aux'
> 'main/SetsMaps/chapterSetsMaps.aux'
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> dftex/updmap/pdftex.map}]) [2] (./topologybook.toc [3] [4] [5]) [6]
> (./main/mainmatter.tex (./main/SetsMaps/chapterSetsMaps.tex
> (./main/SetsMaps/setsmaps-init.tex) (./main/SetsMaps/logic.tex
> Underfull \vbox (badness 10000) has occurred while \output is active [1])
> (./main/SetsMaps/sets.tex [2] [3] [4] [5] [6]
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> Overfull \hbox (38.67267pt too wide) in paragraph at lines 733--734
> \T1/hlh/m/n/10 (-20) verse re-la-tion $[]$ is \T1/hlh/m/it/10 (-20) not \T1/hlh
> /m/n/10 (-20) func-tional be-cause the set $\OMS/hlcy/m/n/10 f [] g$
> [13] [14]) (./main/SetsMaps/maps.tex [15] [16] [17] [18] [19] [20] [21]
> [22] [23] [24] [25] [26] [27] [28]
> Overfull \hbox (1.20296pt too wide) in paragraph at lines 934--935
> []\T1/hlh/m/n/10 (-20) In examples ([][]*[][]) of the subsection ``Injections,
> surjections, and bijections''
> [29] [30] [31]) (./main/SetsMaps/families.tex
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> []\T1/hlh/m/n/10 (-20) The union and in-ter-sec-tion of two sets in the sense o
> f sub-sec-tion ``Union
>
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> \T1/hlh/m/n/10 (-20) Moreover, the for-mu-las in-volv-ing union and in-ter-sec-
> tion in sub-sec-tion ``Union
> [37] [38] [39] [40] [41] [42] [43] [44]
> Overfull \hbox (2.57535pt too wide) in paragraph at lines 909--910
> []\T1/hlh/m/n/10 (-20) Let $\OML/hlcm/m/it/10 n$ \T1/hlh/m/n/10 (-20) be a pos-
> i-tive in-te-ger and let $\OML/hlcm/m/it/10 ÑX[]Ö[]$ \T1/hlh/m/n/10 (-20) be a
> fam-ily of \T1/hlh/m/it/10 (-20) nonempty
> [45]) (./main/SetsMaps/recursion.tex [46] [47] [48] [49] [50] [51] [52])
> (./main/SetsMaps/countable.tex [53]
> Overfull \hbox (3.3389pt too wide) in paragraph at lines 84--88
> \T1/hlh/m/n/10 (-20) Hence the map ob-tained from $\OML/hlcm/m/it/10 h[]$ \T1/h
> lh/m/n/10 (-20) by re-strict-ing its do-main to $\OMS/hlcy/m/n/10 f\T1/hlh/m/n/
> 10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ; n;
> n \OMS/hlcy/m/n/10 Ç
> [54]
> Overfull \hbox (10.72176pt too wide) in paragraph at lines 152--155
> []\T1/hlh/m/n/10 (-20) Now let $\OML/hlcm/m/it/10 n \OMS/hlcy/m/n/10 ^^U \T1/hl
> h/m/n/10 (-20) 1$ and as-sume that each sub-set of $\OMS/hlcy/m/n/10 f\T1/hlh/m
> /n/10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ;
> n\OMS/hlcy/m/n/10 g$
> [55] [56] [57] [58] [59] [60] [61] [62] [63]) (./main/SetsMaps/ordering.tex
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> [79]) (./main/SetsMaps/ordercomplete.tex [80] [81] [82] [83])
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> []\T1/hlh/m/n/10 (-20) The pre-ced-ing proof is a typ-i-cal pro-ce-dure for ap-
> ply-ing Zorn's Lemma.To
> [94] [95])) [96] (./main/MetricSpaces/chapterMetrics.tex
> (./main/MetricSpaces/metrics-init.tex) (./main/MetricSpaces/metrics.tex
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> []\T1/hls/b/n/10 1.9 Ex-am-ple. []\T1/hlh/m/n/10 (-20) Again let $\OML/hlcm/m/i
> t/10 X$ \T1/hlh/m/n/10 (-20) be the set of all con-tin-u-ous func-tions $\OML/h
> lcm/m/it/10 x [] [] Ü\T1/hlh/m/n/10 (-20) 0\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (
> -20) 1\OML/hlcm/m/it/10 á [] \LMR/hlcm/m/n/10 R$\T1/hlh/m/n/10 (-20) .
> [108] [109] [110] [111] [112] [113] [114]
> Overfull \hbox (1.90543pt too wide) in paragraph at lines 1092--1093
> []\T1/hlh/m/n/10 (-20) Are the taxi-cab and max met-rics on $\LMR/hlcm/m/n/10 R
> []$ \T1/hlh/m/n/10 (-20) also translation-invariant?
> [115] [116] [117] [118]) (./main/MetricSpaces/openclosed.tex [119] [120]
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> \OML/hlcm/m/it/10 d[]Ñy[]; y[]Ö \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 d[][]fÑx[]
> Ö; fÑx[]Ö[] \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 dÑx[]; x[]Ö \OMS/hlcy/m/n/10 É
> \OML/hlcm/m/it/10 d[]f[]Ñy[]Ö; f[]Ñy[]Ö[]: []
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> []\T1/hlh/m/n/10 (-20) The met-ric space $\OML/hlcm/m/it/10 ÑÜ\T1/hlh/m/n/10 (-
> 20) 0\OML/hlcm/m/it/10 ; cá; dÖ$ \T1/hlh/m/n/10 (-20) is topo-log-i-cally equiv
> -a-lent to $\OML/hlcm/m/it/10 ÑÜa; bá; d[]Ö$\T1/hlh/m/n/10 (-20) .
>
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> \T1/hlh/m/n/10 (-20) ---the com-pos-ite of a trans-la-tion fol-lowed by a di-la
> -tion or contraction---
> [155] [156]
> Overfull \hbox (0.39265pt too wide) in paragraph at lines 993--995
> []\T1/hlh/m/n/10 (-20) Let $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) be the col
> -lec-tion of all nonempty $\OML/hlcm/m/it/10 d$\T1/hlh/m/n/10 (-20) -closed sub
> -sets of a bounded
> [157] [158]) (./main/MetricSpaces/contconv.texpdfTeX warning (ext4): destinatio
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> []\T1/hlh/m/it/10 (-20) For each $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/it/10 (-20) -
> neighborhood $\OML/hlcm/m/it/10 N$ \T1/hlh/m/it/10 (-20) of $\OML/hlcm/m/it/10
> fÑxÖ$ \T1/hlh/m/it/10 (-20) in $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/it/10 (-20) ther
> e ex-ists some $\OML/hlcm/m/it/10 d$\T1/hlh/m/it/10 (-20) -neighborhood
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> []\T1/hlh/m/n/10 (-20) Assume ([][]3[][]). Let $\OML/hlcm/m/it/10 " > \T1/hlh/m
> /n/10 (-20) 0$. Since $\OML/hlcm/m/it/10 B[]ÑfÑxÖ\T1/hlh/m/n/10 (-20) ; \OML/hl
> cm/m/it/10 d[]Ö$ \T1/hlh/m/n/10 (-20) is a $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/n/1
> 0 (-20) -neighborhood
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> \T1/hlh/m/n/10 (-20) of ad-di-tion and mul-ti-pli-ca-tion, re-spec-tively, are
> $\OML/hlcm/m/it/10 Ñd[]; dÖ$\T1/hlh/m/n/10 (-20) -continuous.
> [178] [179] [180] [181] [182]) (./main/MetricSpaces/complete.tex [183] [184]
> [185]
> Overfull \hbox (2.25098pt too wide) in paragraph at lines 197--199
> \T1/hlh/m/n/10 (-20) For ex-am-ple, any isom-e-try from $\OML/hlcm/m/it/10 ÑX;
> dÖ$ \T1/hlh/m/n/10 (-20) and $\OML/hlcm/m/it/10 ÑY; d[]Ö$ \T1/hlh/m/n/10 (-20)
> is $\OML/hlcm/m/it/10 Ñd; d[]Ö$\T1/hlh/m/n/10 (-20) -uniformly
> )) [186] (./main/TopologicalSpaces/chapterTopological.tex
> (./main/TopologicalSpaces/topological-init.tex)
> (./main/TopologicalSpaces/topologies.tex
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> []\T1/hlh/m/n/10 (-20) (\T1/hlh/m/it/10 (-20) Note: \T1/hlh/m/n/10 (-20) A reg-
> u-lar space, even a reg-u-lar $\OML/hlcm/m/it/10 T[]$\T1/hlh/m/n/10 (-20) -spac
> e, need not be metrizable---
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> Overfull \hbox (15.12009pt too wide) in paragraph at lines 676--701
> \T1/hlh/m/n/10 (-20) de-picts three mem-bers of a set of the form $\OML/hlcm/m/
> it/10 B[]x[]; x[]; x[]; x[] \T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[];
> I[]; I[][]$\T1/hlh/m/n/10 (-20) .]
>
> Overfull \hbox (39.92242pt too wide) in paragraph at lines 676--701
> \T1/hlh/m/n/10 (-20) De-fine $\OMS/hlcy/m/n/10 B$ \T1/hlh/m/n/10 (-20) to be t
> he col-lec-tion of all such sub-sets $\OML/hlcm/m/it/10 B[]x[]; x[]; [] ; x[] \
> T1/hlh/m/n/10 (-20) ; \OML/hlcm/m/it/10 I[]; I[]; [] ; I[][]$
>
> Overfull \hbox (15.45676pt too wide) in paragraph at lines 676--701
> \T1/hlh/m/n/10 (-20) of $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) for all pos-s
> i-ble choices of $\OML/hlcm/m/it/10 k$\T1/hlh/m/n/10 (-20) , of $\OML/hlcm/m/it
> /10 Ñ[]Ö$\T1/hlh/m/n/10 (-20) , and of $\OML/hlcm/m/it/10 Ñ[]Ö$\T1/hlh/m/n/10 (
> -20) .
> [237]
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> [243] [244] [245])) [246]
> (./main/ContinuityConvergence/chapterContinuityConvergence.tex
> (./main/ContinuityConvergence/continuityconvergence-init.tex)
> (./main/ContinuityConvergence/continuous.tex [247]
> Overfull \hbox (13.0625pt too wide) in paragraph at lines 56--59
> \T1/hlh/m/n/10 (-20) map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/10 S\OML/
> hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$ \T1/hlh/m/n/10 (-2
> 0) is also con-tin-u-ous as a map $\OML/hlcm/m/it/10 f [] [] ÑX; \OMS/hlcy/m/n/
> 10 T\OML/hlcm/m/it/10 Ö [] ÑY; \OMS/hlcy/m/n/10 U\OML/hlcm/m/it/10 Ö$\T1/hlh/m/
> n/10 (-20) .
> ) (./main/ContinuityConvergence/homeomorphism.tex [248])
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> Output written on topologybook.pdf (316 pages, 1208256 bytes).
> SyncTeX written on topologybook.synctex.gz.
> Transcript written on topologybook.log.
> Latexmk: Index file 'notation.idx' was written
> Latexmk: Index file 'names.idx' was written
> Latexmk: Index file 'topologybook.idx' was written
> ===========Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> ===========Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> ===========Latexmk: Missing input file: 'notation.gls' from line
> 'No file notation.gls.'
> Latexmk: Missing input file: 'notation.gls' from line
> 'No file notation.gls.'
> ===========Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> ===========Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> Latexmk: Log file says output to 'topologybook.pdf'
> Latexmk: Couldn't find aux file 'front/frontmatter.aux'
> Latexmk: Couldn't find aux file 'front/preface.aux'
> === TeX engine is 'pdfTeX'
> Latexmk: Found bibliography file(s) [mytopologybook.bib mytopologyread.bib topologybook-blx.bib]
> Latexmk: Summary of warnings:
> Latex failed to resolve 9 reference(s)
> Rule 'bibtex topologybook': File changes, etc:
> Changed files, or newly in use since previous run(s):
> 'back/backmatter.aux'
> 'main/Compact/chapterCompact.aux'
> 'main/Connected/chapterConnected.aux'
> 'main/ContinuityConvergence/chapterContinuityConvergence.aux'
> 'main/Embedding/chapterEmbedding.aux'
> 'main/MetricSpaces/chapterMetrics.aux'
> 'main/SetsMaps/chapterSetsMaps.aux'
> 'main/TopologicalSpaces/chapterTopological.aux'
> ------------
> Run number 3 of rule 'bibtex topologybook'
> ------------
> ------------
> Running 'bibtex "topologybook"'
> ------------
> Latexmk: applying rule 'bibtex topologybook'...
> For rule 'bibtex topologybook', running '&run_bibtex( )' ...
> This is BibTeX, Version 0.99d (TeX Live 2017)
> The top-level auxiliary file: topologybook.aux
> The style file: biblatex.bst
> I couldn't open auxiliary file front/frontmatter.aux
> ---line 25 of file topologybook.aux
> : \@input{front/frontmatter.aux
> : }
> I'm skipping whatever remains of this command
> I couldn't open auxiliary file front/preface.aux
> ---line 39 of file topologybook.aux
> : \@input{front/preface.aux
> : }
> I'm skipping whatever remains of this command
> A level-1 auxiliary file: main/SetsMaps/chapterSetsMaps.aux
> A level-1 auxiliary file: main/MetricSpaces/chapterMetrics.aux
> A level-1 auxiliary file: main/TopologicalSpaces/chapterTopological.aux
> A level-1 auxiliary file: main/ContinuityConvergence/chapterContinuityConvergence.aux
> A level-1 auxiliary file: main/Compact/chapterCompact.aux
> A level-1 auxiliary file: main/Connected/chapterConnected.aux
> A level-1 auxiliary file: main/Embedding/chapterEmbedding.aux
> A level-1 auxiliary file: back/backmatter.aux
> Database file #1: topologybook-blx.bib
> Database file #2: mytopologybook.bib
> Database file #3: mytopologyread.bib
> Biblatex version: 3.3
> (There were 2 error messages)
> Latexmk: One or more aux files is missing for bibtex. I'll try
> to get (pdf)latex to remake them.
> Rule 'pdflatex': File changes, etc:
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> 'topologybook.run.xml'
> ------------
> Run number 4 of rule 'pdflatex'
> ------------
> ------------
> Running 'pdflatex --synctex=1 --file-line-error -recorder "topologybook.tex"'
> ------------
> Latexmk: applying rule 'pdflatex'...
> This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017) (preloaded format=pdflatex)
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> (./main/mainmatter.tex (./main/SetsMaps/chapterSetsMaps.tex
> (./main/SetsMaps/setsmaps-init.tex) (./main/SetsMaps/logic.tex
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> Overfull \hbox (38.67267pt too wide) in paragraph at lines 733--734
> \T1/hlh/m/n/10 (-20) verse re-la-tion $[]$ is \T1/hlh/m/it/10 (-20) not \T1/hlh
> /m/n/10 (-20) func-tional be-cause the set $\OMS/hlcy/m/n/10 f [] g$
> [13] [14]) (./main/SetsMaps/maps.tex [15] [16] [17] [18] [19] [20] [21]
> [22] [23] [24] [25] [26] [27] [28]
> Overfull \hbox (1.20296pt too wide) in paragraph at lines 934--935
> []\T1/hlh/m/n/10 (-20) In examples ([][]*[][]) of the subsection ``Injections,
> surjections, and bijections''
> [29] [30] [31]) (./main/SetsMaps/families.tex
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> []\T1/hlh/m/n/10 (-20) The union and in-ter-sec-tion of two sets in the sense o
> f sub-sec-tion ``Union
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> \T1/hlh/m/n/10 (-20) Moreover, the for-mu-las in-volv-ing union and in-ter-sec-
> tion in sub-sec-tion ``Union
> [37] [38] [39] [40] [41] [42] [43] [44]
> Overfull \hbox (2.57535pt too wide) in paragraph at lines 909--910
> []\T1/hlh/m/n/10 (-20) Let $\OML/hlcm/m/it/10 n$ \T1/hlh/m/n/10 (-20) be a pos-
> i-tive in-te-ger and let $\OML/hlcm/m/it/10 ÑX[]Ö[]$ \T1/hlh/m/n/10 (-20) be a
> fam-ily of \T1/hlh/m/it/10 (-20) nonempty
> [45]) (./main/SetsMaps/recursion.tex [46] [47] [48] [49] [50] [51] [52])
> (./main/SetsMaps/countable.tex [53]
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> \T1/hlh/m/n/10 (-20) Hence the map ob-tained from $\OML/hlcm/m/it/10 h[]$ \T1/h
> lh/m/n/10 (-20) by re-strict-ing its do-main to $\OMS/hlcy/m/n/10 f\T1/hlh/m/n/
> 10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ; n;
> n \OMS/hlcy/m/n/10 Ç
> [54]
> Overfull \hbox (10.72176pt too wide) in paragraph at lines 152--155
> []\T1/hlh/m/n/10 (-20) Now let $\OML/hlcm/m/it/10 n \OMS/hlcy/m/n/10 ^^U \T1/hl
> h/m/n/10 (-20) 1$ and as-sume that each sub-set of $\OMS/hlcy/m/n/10 f\T1/hlh/m
> /n/10 (-20) 1\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (-20) 2\OML/hlcm/m/it/10 ; [] ;
> n\OMS/hlcy/m/n/10 g$
> [55] [56] [57] [58] [59] [60] [61] [62] [63]) (./main/SetsMaps/ordering.tex
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> []\T1/hlh/m/n/10 (-20) The pre-ced-ing proof is a typ-i-cal pro-ce-dure for ap-
> ply-ing Zorn's Lemma.To
> [94] [95])) [96] (./main/MetricSpaces/chapterMetrics.tex
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> []\T1/hls/b/n/10 1.9 Ex-am-ple. []\T1/hlh/m/n/10 (-20) Again let $\OML/hlcm/m/i
> t/10 X$ \T1/hlh/m/n/10 (-20) be the set of all con-tin-u-ous func-tions $\OML/h
> lcm/m/it/10 x [] [] Ü\T1/hlh/m/n/10 (-20) 0\OML/hlcm/m/it/10 ; \T1/hlh/m/n/10 (
> -20) 1\OML/hlcm/m/it/10 á [] \LMR/hlcm/m/n/10 R$\T1/hlh/m/n/10 (-20) .
> [108] [109] [110] [111] [112] [113] [114]
> Overfull \hbox (1.90543pt too wide) in paragraph at lines 1092--1093
> []\T1/hlh/m/n/10 (-20) Are the taxi-cab and max met-rics on $\LMR/hlcm/m/n/10 R
> []$ \T1/hlh/m/n/10 (-20) also translation-invariant?
> [115] [116] [117] [118]) (./main/MetricSpaces/openclosed.tex [119] [120]
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> \OML/hlcm/m/it/10 d[]Ñy[]; y[]Ö \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 d[][]fÑx[]
> Ö; fÑx[]Ö[] \OMS/hlcy/m/n/10 É \OML/hlcm/m/it/10 dÑx[]; x[]Ö \OMS/hlcy/m/n/10 É
> \OML/hlcm/m/it/10 d[]f[]Ñy[]Ö; f[]Ñy[]Ö[]: []
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> []\T1/hlh/m/n/10 (-20) The met-ric space $\OML/hlcm/m/it/10 ÑÜ\T1/hlh/m/n/10 (-
> 20) 0\OML/hlcm/m/it/10 ; cá; dÖ$ \T1/hlh/m/n/10 (-20) is topo-log-i-cally equiv
> -a-lent to $\OML/hlcm/m/it/10 ÑÜa; bá; d[]Ö$\T1/hlh/m/n/10 (-20) .
>
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> \T1/hlh/m/n/10 (-20) ---the com-pos-ite of a trans-la-tion fol-lowed by a di-la
> -tion or contraction---
> [155] [156]
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> []\T1/hlh/m/n/10 (-20) Let $\OMS/hlcy/m/n/10 F$ \T1/hlh/m/n/10 (-20) be the col
> -lec-tion of all nonempty $\OML/hlcm/m/it/10 d$\T1/hlh/m/n/10 (-20) -closed sub
> -sets of a bounded
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> []\T1/hlh/m/it/10 (-20) For each $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/it/10 (-20) -
> neighborhood $\OML/hlcm/m/it/10 N$ \T1/hlh/m/it/10 (-20) of $\OML/hlcm/m/it/10
> fÑxÖ$ \T1/hlh/m/it/10 (-20) in $\OML/hlcm/m/it/10 Y$ \T1/hlh/m/it/10 (-20) ther
> e ex-ists some $\OML/hlcm/m/it/10 d$\T1/hlh/m/it/10 (-20) -neighborhood
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> []\T1/hlh/m/n/10 (-20) Assume ([][]3[][]). Let $\OML/hlcm/m/it/10 " > \T1/hlh/m
> /n/10 (-20) 0$. Since $\OML/hlcm/m/it/10 B[]ÑfÑxÖ\T1/hlh/m/n/10 (-20) ; \OML/hl
> cm/m/it/10 d[]Ö$ \T1/hlh/m/n/10 (-20) is a $\OML/hlcm/m/it/10 d[]$\T1/hlh/m/n/1
> 0 (-20) -neighborhood
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> \T1/hlh/m/n/10 (-20) of ad-di-tion and mul-ti-pli-ca-tion, re-spec-tively, are
> $\OML/hlcm/m/it/10 Ñd[]; dÖ$\T1/hlh/m/n/10 (-20) -continuous.
> [178] [179] [180] [181] [182]) (./main/MetricSpaces/complete.tex [183] [184]
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> \T1/hlh/m/n/10 (-20) For ex-am-ple, any isom-e-try from $\OML/hlcm/m/it/10 ÑX;
> dÖ$ \T1/hlh/m/n/10 (-20) and $\OML/hlcm/m/it/10 ÑY; d[]Ö$ \T1/hlh/m/n/10 (-20)
> is $\OML/hlcm/m/it/10 Ñd; d[]Ö$\T1/hlh/m/n/10 (-20) -uniformly
> )) [186] (./main/TopologicalSpaces/chapterTopological.tex
> (./main/TopologicalSpaces/topological-init.tex)
> (./main/TopologicalSpaces/topologies.tex
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> []\T1/hlh/m/n/10 (-20) metrically equiv-a-lent met-ric spaces,
>
> Overfull \hbox (2.2026pt too wide) in paragraph at lines 544--546
> []\T1/hlh/m/n/10 (-20) neighborhood, [][]\T1/hlh/b/it/10 200[][]\T1/hlh/m/n/10
> (-20) , [][]200[][]--[][]202[][], [][]228[][],
>
> Overfull \hbox (3.06833pt too wide) in paragraph at lines 555--557
> []\T1/hlh/m/n/10 (-20) Niemytzki plane (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/
> 10 (-20) tan-gent disk
> [305]
> Overfull \hbox (9.05663pt too wide) in paragraph at lines 574--575
> []| \T1/hlh/m/n/10 (-20) in second-countable space, [][]275[][]
>
> Overfull \hbox (1.59937pt too wide) in paragraph at lines 592--593
> []| \T1/hlh/m/n/10 (-20) and mul-ti-plica-tive in-verse, [][]20[][]
>
> Overfull \hbox (4.32907pt too wide) in paragraph at lines 600--602
> []\T1/hlh/m/n/10 (-20) order topol-ogy, [][]\T1/hlh/b/it/10 235[][]\T1/hlh/m/n/
> 10 (-20) , [][]235[][]--[][]236[][], [][]245[][]
>
> Overfull \hbox (5.82869pt too wide) in paragraph at lines 609--611
> \T1/hlh/m/n/10 (-20) der-ing; pre-order-ing; strict
>
> Overfull \hbox (20.25978pt too wide) in paragraph at lines 609--611
> \T1/hlh/m/n/10 (-20) weak or-der-ing; well-ordering)
> [306]
> Overfull \hbox (2.26106pt too wide) in paragraph at lines 728--730
> \T1/hlh/m/n/10 (-20) func-tional re-la-tion, or-der
> [307]
> Overfull \hbox (0.88599pt too wide) in paragraph at lines 751--753
> []\T1/hlh/m/n/10 (-20) second-category set (\T1/hlh/m/it/10 (-20) see \T1/hlh/
> m/n/10 (-20) non-mea-
>
> Overfull \hbox (1.02753pt too wide) in paragraph at lines 753--754
> []\T1/hlh/m/n/10 (-20) second-countable space, [][]\T1/hlh/b/it/10 239[][]\T1/h
> lh/m/n/10 (-20) , [][]239[][]
>
> Overfull \hbox (0.32431pt too wide) in paragraph at lines 769--771
> []\T1/hlh/m/n/10 (-20) sequential com-pact-ness, [][]275[][], [][]277[][]
>
> Overfull \hbox (10.40741pt too wide) in paragraph at lines 777--779
> []\T1/hlh/m/n/10 (-20) smaller topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/
> n/10 (-20) coarser topol-
>
> Overfull \hbox (1.25479pt too wide) in paragraph at lines 783--785
> []\T1/hlh/m/n/10 (-20) space (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-20) t
> opo-log-i-cal space, met-
>
> Overfull \hbox (6.31657pt too wide) in paragraph at lines 787--788
> []\T1/hlh/m/n/10 (-20) statement (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n/10 (-2
> 0) pred-i-cate,sentence)
>
> Overfull \hbox (2.04988pt too wide) in paragraph at lines 788--790
> []\T1/hlh/m/n/10 (-20) strict or-der-ing (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/
> n/10 (-20) strict di-rected
>
> Overfull \hbox (2.03561pt too wide) in paragraph at lines 788--790
> \T1/hlh/m/n/10 (-20) or-der-ing; strict par-tial or-
>
> Overfull \hbox (3.09906pt too wide) in paragraph at lines 792--794
> []\T1/hlh/m/n/10 (-20) stronger topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m
> /n/10 (-20) finer topol-
> [308]
> Overfull \hbox (21.70116pt too wide) in paragraph at lines 850--852
> []\T1/hlh/m/n/10 (-20) topologically equiv-a-lent met-ric spaces,
>
> Overfull \hbox (2.09372pt too wide) in paragraph at lines 862--863
> []| \T1/hlh/m/n/10 (-20) gen-er-ated by a col-lec-tion, [][]234[][]
>
> Overfull \hbox (2.37599pt too wide) in paragraph at lines 873--874
> []\T1/hlh/m/n/10 (-20) totally bounded met-ric space, [][]\T1/hlh/b/it/10 273[]
> []
>
> Overfull \hbox (2.416pt too wide) in paragraph at lines 902--903
> []| \T1/hlh/m/n/10 (-20) on com-pact met-ric space, [][]279[][]
> [309]
> Overfull \hbox (0.584pt too wide) in paragraph at lines 908--909
> []| \T1/hlh/m/n/10 (-20) of a collection of sets, [][]\T1/hlh/b/it/10 39[][]\T1
> /hlh/m/n/10 (-20) , [][]39[][]--
>
> Overfull \hbox (8.61229pt too wide) in paragraph at lines 935--937
> []\T1/hlh/m/n/10 (-20) weaker topol-ogy (\T1/hlh/m/it/10 (-20) see \T1/hlh/m/n
> /10 (-20) coarser topol-
> [310]))) (./topologybook.aux
> No file front/frontmatter.aux.
> No file front/preface.aux.
> (./main/SetsMaps/chapterSetsMaps.aux) (./main/MetricSpaces/chapterMetrics.aux)
> (./main/TopologicalSpaces/chapterTopological.aux)
> (./main/ContinuityConvergence/chapterContinuityConvergence.aux)
> (./main/Compact/chapterCompact.aux) (./main/Connected/chapterConnected.aux)
> (./main/Embedding/chapterEmbedding.aux) (./back/backmatter.aux))
> Dependency list written on topologybook.dep.
>
> LaTeX Warning: There were undefined references.
>
> )
> (see the transcript file for additional information)pdfTeX warning (dest): name
> {cite.0 at GoldbergReal1976} has been referenced but does not exist, replaced by a
> fixed one
>
> pdfTeX warning (dest): name{cite.0 at BoasPrimerReal1996} has been referenced but
> does not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at KConradIsometries} has been referenced but d
> oes not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at FlemingSeveralVars2Ed} has been referenced b
> ut does not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at ChrisCooperIsometries3D} has been referenced
> but does not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at ChrisCooperIsometries} has been referenced b
> ut does not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at JacobBaileyLinearAlgebra} has been reference
> d but does not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at GaillardZorn2017} has been referenced but do
> es not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at GraysonZorn2007} has been referenced but doe
> s not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at KneserZorn1950} has been referenced but does
> not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at Suppes1972} has been referenced but does not
> exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at Bernays1991} has been referenced but does no
> t exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at EisenbergSets1971} has been referenced but d
> oes not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at BourbakiSets2004} has been referenced but do
> es not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at PinterSets2014} has been referenced but does
> not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at LakinsMathReasoning2016} has been referenced
> but does not exist, replaced by a fixed one
>
> pdfTeX warning (dest): name{cite.0 at EisenbergMathMethod1996} has been referenced
> but does not exist, replaced by a fixed one
>
> {/usr/local/texlive/2017/texmf-dist/fonts/enc/dvips/base/8r.enc}</Users/murray/
> Library/texmf/fonts/type1/bh/lucida/lbd.pfb></Users/murray/Library/texmf/fonts/
> type1/bh/lucida/lbdi.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbi
> .pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbma.pfb></Users/murray
> /Library/texmf/fonts/type1/bh/lucida/lbme.pfb></Users/murray/Library/texmf/font
> s/type1/bh/lucida/lbmo.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/l
> bmr.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lbms.pfb></Users/mur
> ray/Library/texmf/fonts/type1/bh/lucida/lbmsd.pfb></Users/murray/Library/texmf/
> fonts/type1/bh/lucida/lbr.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucid
> a/lsd.pfb></Users/murray/Library/texmf/fonts/type1/bh/lucida/lsdi.pfb></Users/m
> urray/Library/texmf/fonts/type1/bh/lucida/lsi.pfb></Users/murray/Library/texmf/
> fonts/type1/bh/lucida/lsr.pfb></usr/local/texlive/2017/texmf-dist/fonts/type1/p
> ublic/xypic/xyatip10.pfb></usr/local/texlive/2017/texmf-dist/fonts/type1/public
> /xypic/xybtip10.pfb>
> Output written on topologybook.pdf (316 pages, 1208256 bytes).
> SyncTeX written on topologybook.synctex.gz.
> Transcript written on topologybook.log.
> Latexmk: Index file 'notation.idx' was written
> Latexmk: Index file 'names.idx' was written
> Latexmk: Index file 'topologybook.idx' was written
> ===========Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> ===========Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> ===========Latexmk: Missing input file: 'notation.gls' from line
> 'No file notation.gls.'
> Latexmk: Missing input file: 'notation.gls' from line
> 'No file notation.gls.'
> ===========Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> Latexmk: Missing input file: 'front/frontmatter.aux' from line
> 'No file front/frontmatter.aux.'
> ===========Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> Latexmk: Missing input file: 'front/preface.aux' from line
> 'No file front/preface.aux.'
> Latexmk: Log file says output to 'topologybook.pdf'
> Latexmk: Couldn't find aux file 'front/frontmatter.aux'
> Latexmk: Couldn't find aux file 'front/preface.aux'
> === TeX engine is 'pdfTeX'
> Latexmk: Found bibliography file(s) [mytopologybook.bib mytopologyread.bib topologybook-blx.bib]
> Latexmk: Summary of warnings:
> Latex failed to resolve 9 reference(s)
> Latexmk: All targets (topologybook.pdf) are up-to-date
>
>
> =========== END console file ================
> ---
> Murray Eisenberg murrayeisenberg at gmail.com <mailto:murrayeisenberg at gmail.com>
> 503 King Farm Blvd #101 Home (240)-246-7240
> Rockville, MD 20850-6667 Mobile (413)-427-5334
>
>
---
Murray Eisenberg murrayeisenberg at gmail.com
503 King Farm Blvd #101 Home (240)-246-7240
Rockville, MD 20850-6667 Mobile (413)-427-5334
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