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.

$\blacksquare$

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $5$: Compact spaces: $5.4$: Properties of compact spaces: Proposition $5.4.2$