# Arens-Fort Space is Lindelöf

## Theorem

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

Then $T$ is a Lindelöf space.

## Proof

We have:

The Arens-Fort Space is Sigma-Compact.
A $\sigma$-compact space is Lindelöf.

$\blacksquare$