Compact Subspace of Hausdorff Space is Closed/Corollary

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.

$\blacksquare$