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.