Arens-Fort Space is not Compact

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Theorem

Let $T = \left({S, \tau}\right)$ be the Arens-Fort space.


Then $T$ is not a compact space.


Proof

We have:

The Arens-Fort Space is not Weakly Locally Compact.
A Compact Space is Weakly Locally Compact.

$\blacksquare$


Sources