# Discrete Space is Fully Normal

## Theorem

Let $T = \struct {S, \tau}$ be a discrete topological space.

Then $T$ is fully normal.

## Proof

We have that a Discrete Space is fully $T_4$.

Then we note that from Discrete Space satisfies all Separation Properties, a discrete space is a $T_1$ (Fréchet) space.

Therefore, by definition, $T$ is fully normal.

$\blacksquare$