Modified Fort Space is not Totally Separated

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

Then $T$ is not totally separated.

Proof
We have:
 * Totally Separated Space is Completely Hausdorff and Urysohn
 * Completely Hausdorff Space is Hausdorff Space

But we have:
 * Modified Fort Space is not Hausdorff

The result follows from Modus Tollendo Tollens.