# Modified Fort Space is Totally Disconnected

## Theorem

Let $T = \struct {S, \tau_{a, b} }$ be a modified Fort space.

Then $T$ is totally disconnected.

## Proof

We have:

Modified Fort Space is Scattered
Modified Fort Space is $T_1$

We also have:

Scattered $T_1$ Space is Totally Disconnected

Hence the result.

$\blacksquare$