\relax 
\providecommand\babel@aux[2]{}
\@nameuse{bbl@beforestart}
\catcode `"\active 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\babel@aux{dutch}{}
\@writefile{toc}{\contentsline {chapter}{\numberline {}Introductie}{5}{chapter*.2}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {}Conventies}{5}{section*.3}\protected@file@percent }
\citation{ArbProd}
\citation{ArbProd}
\citation{Tycho}
\@writefile{toc}{\contentsline {chapter}{\numberline {1}De Producttopologie}{7}{chapter.1}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {1.1}Eindige producten}{7}{section.1.1}\protected@file@percent }
\newlabel{sec:eindigeProd}{{1.1}{7}{Eindige producten}{section.1.1}{}}
\newlabel{def:eindigProd}{{1.1}{7}{}{theorem.1.1}{}}
\citation{ArbProd}
\citation{ArbProd}
\newlabel{lemma:eqprod}{{1.2}{8}{}{theorem.1.2}{}}
\newlabel{ref:nieteqprod}{{1.3}{8}{}{theorem.1.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {1.2}Doostopologie}{8}{section.1.2}\protected@file@percent }
\newlabel{def:doostopologie}{{1.4}{8}{}{theorem.1.4}{}}
\newlabel{secComponentDoos}{{1.5}{8}{Componentsgewijze continuïteit}{theorem.1.5}{}}
\citation{ArbProd}
\citation{ArbProd}
\newlabel{secCompactDoos}{{1.6}{9}{Compactheid}{theorem.1.6}{}}
\@writefile{toc}{\contentsline {section}{\numberline {1.3}Producttopologie}{9}{section.1.3}\protected@file@percent }
\newlabel{def:producttopology}{{1.7}{9}{}{theorem.1.7}{}}
\newlabel{basisProduct}{{1.8}{9}{}{theorem.1.8}{}}
\newlabel{productBasis}{{1.1}{9}{}{equation.1.3.1}{}}
\citation{ArbProd}
\citation{ArbProd}
\citation{ArbProd}
\newlabel{CompContImpliesCont}{{1.10}{10}{}{theorem.1.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.1}Aftelbare producten}{10}{subsection.1.3.1}\protected@file@percent }
\newlabel{metriseerbaar}{{1.11}{10}{}{theorem.1.11}{}}
\citation{Tycho}
\citation{Tycho}
\citation{Tycho}
\citation{Tycho}
\@writefile{toc}{\contentsline {section}{\numberline {1.4}Stelling van Tychonov}{11}{section.1.4}\protected@file@percent }
\newlabel{secTychonov}{{1.4}{11}{Stelling van Tychonov}{section.1.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.1}Het keuzeaxioma en het lemma van Zorn}{11}{subsection.1.4.1}\protected@file@percent }
\citation{Tycho}
\citation{Tycho}
\citation{Nets}
\citation{Nets}
\citation{Tycho}
\citation{Tycho}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.2}Karakterisatie van compacte ruimtes}{12}{subsection.1.4.2}\protected@file@percent }
\newlabel{compactIsAccumulatie}{{1.19}{12}{}{theorem.1.19}{}}
\citation{Tycho}
\citation{Tycho}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.3}Extra beweringen over netten}{13}{subsection.1.4.3}\protected@file@percent }
\newlabel{AccIsConv}{{1.22}{13}{}{theorem.1.22}{}}
\citation{Tycho}
\newlabel{DeelZelfde}{{1.23}{14}{}{theorem.1.23}{}}
\newlabel{CompConvNet}{{1.24}{14}{}{theorem.1.24}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.4}Bewijs van Tychonov}{14}{subsection.1.4.4}\protected@file@percent }
\newlabel{Tbovengrens}{{1.25}{14}{}{theorem.1.25}{}}
\newlabel{m_k}{{1.3}{15}{Bewijs van Tychonov}{equation.1.4.3}{}}
\newlabel{MaxAccumulatie}{{1.26}{15}{}{theorem.1.26}{}}
\newlabel{SmallerHasBigger}{{1.27}{15}{}{theorem.1.27}{}}
\citation{ProFin}
\citation{YouTube}
\citation{YouTube}
\citation{ProFin}
\citation{ProFin}
\citation{ProFin}
\@writefile{toc}{\contentsline {chapter}{\numberline {2}Pro-eindige verzamelingen}{17}{chapter.2}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {2.1}Definitie en voorbeelden}{17}{section.2.1}\protected@file@percent }
\newlabel{EigenlijkLichtProEindig}{{2.5}{17}{}{theorem.2.5}{}}
\citation{YouTube}
\citation{YouTube}
\newlabel{ProEindigCompContIsCont}{{2.6}{18}{}{theorem.2.6}{}}
\newlabel{Ninfty}{{2.7}{18}{}{theorem.2.7}{}}
\citation{YouTube}
\newlabel{explicit}{{2.1}{19}{}{equation.2.1.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.2}Karakterisatie van Pro-eindige verzamelingen}{19}{section.2.2}\protected@file@percent }
\newlabel{ProEindigHaus}{{2.9}{19}{}{theorem.2.9}{}}
\newlabel{ProEindigComp}{{2.10}{20}{}{theorem.2.10}{}}
\citation{YouTube}
\citation{Condensed}
\@writefile{toc}{\contentsline {chapter}{\numberline {3}Gecondenseerde verzamelingen}{21}{chapter.3}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\citation{Yoneda}
\@writefile{toc}{\contentsline {section}{\numberline {3.1}Definitie, voorbeelden en Yoneda}{22}{section.3.1}\protected@file@percent }
\newlabel{LightCond}{{3.2}{22}{}{theorem.3.2}{}}
\newlabel{SingleCond}{{3.5}{22}{}{theorem.3.5}{}}
\citation{Yoneda}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.1}Yoneda}{23}{subsection.3.1.1}\protected@file@percent }
\newlabel{GevolgYoneda}{{3.7}{23}{}{theorem.3.7}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3.2}De gecondenseerde analogonsfunctor}{23}{section.3.2}\protected@file@percent }
\newlabel{commutatie}{{3.1}{24}{De gecondenseerde analogonsfunctor}{equation.3.2.1}{}}
\newlabel{ASingle}{{3.13}{24}{}{theorem.3.13}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3.3}De topologische benaderingsfunctor}{25}{section.3.3}\protected@file@percent }
\newlabel{LinksGeadj}{{3.18}{26}{}{theorem.3.18}{}}
\citation{Seq}
\newlabel{commutatieAlpha}{{3.2}{27}{De topologische benaderingsfunctor}{equation.3.3.2}{}}
\newlabel{commbov}{{3.3}{27}{De topologische benaderingsfunctor}{equation.3.3.3}{}}
\newlabel{commond}{{3.4}{27}{De topologische benaderingsfunctor}{equation.3.3.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3.4}Sequentiele ruimtes}{27}{section.3.4}\protected@file@percent }
\newlabel{proAllSeqClosed}{{3.23}{28}{}{theorem.3.23}{}}
\newlabel{thClosedIsSeq}{{3.24}{28}{}{theorem.3.24}{}}
\newlabel{lemSeqCPreGes}{{3.25}{28}{}{theorem.3.25}{}}
\newlabel{cor:AStarTopIsA}{{3.26}{29}{}{theorem.3.26}{}}
\newlabel{proAllSeqClosed}{{3.23}{29}{}{theorem.3.27}{}}
\bibcite{ArbProd}{1}
\bibcite{Nets}{2}
\bibcite{Tycho}{3}
\bibcite{ProFin}{4}
\bibcite{YouTube}{5}
\bibcite{Yoneda}{6}
\bibcite{Condensed}{7}
\bibcite{Seq}{8}