# Compact Space is Weakly Locally Compact/Proof 3

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## Theorem

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

Then $T$ is a weakly locally compact.

## Proof

Follows directly from:

- Compact Space is Weakly $\sigma$-Locally Compact
- a weakly $\sigma$-locally compact space is weakly locally compact by definition.

$\blacksquare$