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54-00-IndexOfPropertiesOfTopologicalSpaces.tex
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54-00-IndexOfPropertiesOfTopologicalSpaces.tex
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\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{IndexOfPropertiesOfTopologicalSpaces}
\pmcreated{2013-03-22 14:39:29}
\pmmodified{2013-03-22 14:39:29}
\pmowner{rspuzio}{6075}
\pmmodifier{rspuzio}{6075}
\pmtitle{index of properties of topological spaces}
\pmrecord{29}{36251}
\pmprivacy{1}
\pmauthor{rspuzio}{6075}
\pmtype{Topic}
\pmcomment{trigger rebuild}
\pmclassification{msc}{54-00}
\endmetadata
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%%%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
\begin{document}
\PMlinkescapeword{Properties}
\PMlinkescapeword{separated}
\PMlinkescapetext{The puropse of this meta-entry is to list all topological properties discussed in this encyclopaedia (or soon to be added). The properties have been classified into several broad categories; within each category, they have been listed alphabetically. For consistency, the adjectival forms of terms have been used whenever possible. When more than one term appears on a single line, this signifies that the terms are synonyms. For further information on any topic, please click on the appropriate link.}
\centerline{\bf Topological axioms}
\begin{itemize}
\item topological structures on sets
\item continuous maps
\item categories, functors and natural transformations
\end{itemize}
\centerline{\bf Compactness Properties}
\begin{itemize}
\item compact
\item countably compact
\item \PMlinkname{Lindel\"of}{Lindelof}, \PMlinkname{finally compact}{Lindelof}
\item locally compact
\item metacompact
\item paracompact
\item strongly locally compact
\item sequentially compact
\item \PMlinkname{$\sigma$-compact}{SigmaCompact}
\item $\sigma$-locally compact
\item \PMlinkname{weakly countably compact}{LimitPointCompact}, limit point compact
\end{itemize}
\centerline {\bf Countability Properties}
\begin{itemize}
\item \PMlinkname{first countable}{FirstCountable}
\item \PMlinkname{second countable}{SecondCountable}
\item separable
\end{itemize}
\centerline {\bf Connectedness Properties}
\begin{itemize}
\item biconnected
\item arc connected
\item \PMlinkname{connected}{ConnectedSpace}
\item connected im kleinen
\item extremally disconnected
\item hyperconnected
\item locally arc connected
\item locally connected
\item locally path connected
\item path-connected
\item punctiform
\item scattered
\item totally disconnected
\item totally path disconnected
\item totally separated
\item ultraconnected
\end{itemize}
\centerline \PMlinkescapetext{{\bf Contractibility Proprties}}
\begin{itemize}
\item absolute retract
\item absolute neighborhood retract
\item contractible to a point
\end{itemize}
\centerline{\PMlinkescapetext{\bf Homotopic properties}}
\begin{itemize}
\item locally simply connected
\item semi-locally simply connected
\item simply connected
\item locally homeomorphic and covering spaces
\item fibrations
\item homotopy groups
\item homotopy as a functor
\item homotopy type
\item lifting properties of fibrations
\end{itemize}
\centerline{\PMlinkname{\bf Separation Properties}{SeparationAxioms}}
\begin{itemize}
\item completely normal
\item completely regular, Tychonoff
\item fully normal
\item \PMlinkname{fully $T_4$}{FullyT4}
\item normal
\item perfectly $T_4$
\item perfectly normal
\item regular
\item semiregular
\item \PMlinkname{$T_0$}{T0Space}, \PMlinkname{Kolmogorov}{T0Space}
\item \PMlinkname{$T_1$}{T1Space}, \PMlinkname{Fr\'echet}{T1Space}
\item \PMlinkname{$T_2$}{T2Space}, \PMlinkname{Hausdorff}{T2Space}
\item \PMlinkname{$T_{2 \frac12}$}{CompletelyHaussdorff}, completely Hausdorff
\item \PMlinkname{$T_3$}{SeparationAxioms}
\item \PMlinkname{$T_{3 \frac12}$}{SeparationAxioms}
\item \PMlinkname{$T_4$}{SeparationAxioms}
\item \PMlinkname{$T_5$}{SeparationAxioms}
\item Urysohn, functionally Hausdorff
\end{itemize}
\centerline{\bf Subset Properties}
\begin{itemize}
\item open
\item closed
\item clopen
\item regular open
\item \PMlinkname{regular closed}{RegularOpenSet}
\item locally closed
\item dense
\item nowhere dense
\item meager
\item residual
\item \PMlinkname{separated sets}{Separated}
\item \PMlinkname{completely separated sets}{CompletelySeparated}
\end{itemize}
\centerline{\bf Topological groups}
\begin{itemize}
\item full subgroup
\end{itemize}
\centerline{\bf Homology}
%%%%%
%%%%%
\end{document}