Modified Fort Space is not Locally Connected

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

Then $T$ is not locally connected.

Proof
We have:
 * Modified Fort Space is Totally Disconnected
 * Totally Disconnected and Locally Connected Space is Discrete

We also have:
 * Modified Fort Space is not $T_2$
 * Discrete Space satisfies all Separation Properties

Hence modified Fort space is not the discrete space, and the result follows.