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Version 6 |
| \PMlinkescapeword{corollary} |
\PMlinkescapeword{corollary} |
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| Let $X$ be a normal topological space, and let $C,D\subseteq X$ be disjoint closed nonempty subsets. Then there is a continuous function $f\colon X\rightarrow [0,1]$ such that $f(C) = \{0\}$ and $f(D) = \{1\}$. |
Let $X$ be a normal topological space, and let $C,D\subseteq X$ be disjoint closed nonempty subsets. Then there is a continuous function $f\colon X\rightarrow [0,1]$ such that $f(C) = \{0\}$ and $f(D) = \{1\}$. |
| (Any such function is called an \emph{Urysohn function}.) |
(Any such function is called an \emph{Urysohn function}.) |
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A corollary is that normal \PMlinkname{$T_1$}{T1Space} spaces are completely regular.
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A corollary is that normal Hausdorff spaces are completely regular.
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