Modified Fort Space is Totally Disconnected

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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.

$\blacksquare$


Sources