$T4$ spaceT4Space2004-10-08 10:20:022004-10-08 10:28:34Definition% this is the default PlanetMath preamble. as your knowledge
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\newtheorem{cor}{Corollary}\begin{defn} \cite{steen}
Suppose $X$ is a topological space. Further, suppose that
for any two disjoint
closed sets $A,B\subseteq X$, there are two disjoint open sets
$U$ and $V$ such that $A\subseteq U$ and $B\subseteq V$. Then we say
that $X$ is a \emph{$T_4$ space}.
\end{defn}
\subsubsection*{Notes}
It should be pointed out that there is no standard convention
for separation axioms in topology. The above definition follows
\cite{steen}. However, in some references (e.g. \cite{kelley})
the meaning of $T_4$ and normal are exchanged.
\begin{thebibliography}{9}
\bibitem{steen} L.A. Steen, J.A.Seebach, Jr.,
\emph{Counterexamples in topology},
Holt, Rinehart and Winston, Inc., 1970.
\bibitem{kelley}
J.L. Kelley, \emph{General Topology}, D. van Nostrand Company, Inc., 1955.
\end{thebibliography}