54-00-CompletelyNormal.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{CompletelyNormal}
\pmcreated{2013-03-22 12:13:51}
\pmmodified{2013-03-22 12:13:51}
\pmowner{Mathprof}{13753}
\pmmodifier{Mathprof}{13753}
\pmtitle{completely normal}
\pmrecord{7}{31606}
\pmprivacy{1}
\pmauthor{Mathprof}{13753}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{54-00}
\pmsynonym{complete normality}{CompletelyNormal}
%\pmkeywords{topology}
\pmrelated{NormalTopologicalSpace}

\endmetadata

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\usepackage{amsmath}
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\begin{document}
Let $X$ be a topological space.  $X$ is said to be \emph{\PMlinkescapetext{completely normal}} if whenever $A,B\subseteq X$ with $A\cap\overline{B}=\overline{A}\cap B=\emptyset$, then there are disjoint open sets $U$ and $V$ such that $A\subseteq U$ and $B\subseteq V$.

Equivalently, a topological space $X$ is \PMlinkescapetext{completely normal} if and only if every subspace is normal.
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