# Arens-Fort Space is not Weakly Locally Compact

## Theorem

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

Then $T$ is not a weakly locally compact space.

## Proof

So $\left({0, 0}\right)$ is a point in $S$ which is not contained in a compact neighborhood.

Hence, by definition, $T$ is not weakly locally compact.

$\blacksquare$