# Arens-Fort Space is Totally Separated

## Theorem

Let $T = \struct {S, \tau}$ be the Arens-Fort space.

Then $T$ is totally separated.

## Proof

We have that:

The Arens-Fort Space is Zero Dimensional.
The Arens-Fort Space is $T_1$ and so by $T_1$ Space is $T_0$ Space is a $T_0$ (Kolmogorov) space.

Then we have that a Zero Dimensional $T_0$ Space is Totally Separated.

$\blacksquare$