Modified Fort Space is not Totally Separated

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

Then $T$ is not totally separated.


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.