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