# Arens-Fort Space is not Compact

## 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.

$\blacksquare$