Show that every closed subset of a normal space X space is normal?
What is a good approach to this problem?
2026-03-31 10:04:07.1774951447
Closed Subsets on Normal Spaces
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Let $Y=\bar Y\subset X$ and $A,B \subset Y $ disjoint closed sets. Then $A$ and $B$ are closed in $X$. Since $X$ is normal, $\exists U,V \subset X$ open sets such that $A \subset U$, $B \subset V$ and $U \cap V $=$\emptyset$.
What can you say about $U´=U \cap Y$ and $V´=V \cap Y$?