Discrete Space is Totally Disconnected

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

Then $T$ is totally disconnected.

Proof
Follows from:


 * Discrete Space is Extremally Disconnected
 * Extremally Disconnected Space is Totally Separated
 * Totally Separated Space is Totally Disconnected