# Arens-Fort Space is Separable

## Theorem

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

Then $T$ is a separable space.

## Proof

We have that the Arens-Fort space is an expansion of a countable Fort space.

So $S$ is countable.

The result follows from Countable Space is Separable.

$\blacksquare$