Compact Space is Weakly Sigma-Locally Compact

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Theorem

Let $T = \struct {S, \tau}$ be a compact space.


Then $T$ is a weakly $\sigma$-locally compact space.


Proof

Let $T = \struct {S, \tau}$ be a compact space.

We have that:

Compact Space is Sigma-Compact
Compact Space is Weakly Locally Compact

Hence by definition $T$ is weakly $\sigma$-locally compact space.

$\blacksquare$


Sources