Compact Hausdorff Space is Locally Compact/Proof 1

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Theorem

Let $T = \left({S, \tau}\right)$ be a Hausdorff space which is compact.


Then $T$ is locally compact.


Proof

By Compact Space is Weakly Locally Compact, $T$ is weakly locally compact.

Thus $T$ is a locally compact Hausdorff space.

$\blacksquare$