# 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.

$\blacksquare$