Compact Subspace of Hausdorff Space is Closed/Corollary

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Corollary to Compact Subspace of Hausdorff Space is Closed

A finite subspace of a Hausdorff space is closed.


Proof

Follows directly from:

Finite Topological Space is Compact

and:

Compact Subspace of Hausdorff Space is Closed.

$\blacksquare$


Sources