Discrete Space is Locally Connected

Theorem
Let $T = \left({S, \tau}\right)$ be a discrete topological space.

Then $T$ is locally connected.

Proof
Let $T = \left({S, \tau}\right)$ be a discrete space.

From Discrete Space is Locally Path-Connected, $T$ is locally path-connected.

From Locally Path-Connected Space is Locally Connected, it follows that $T$ is locally connected.