# Metric Space is Fully Normal

## Theorem

Let $M = \struct {A, d}$ be a metric space.

Then $M$ is a fully normal space.

## Proof

We have that a metric space is fully $T_4$.

We also have that a metric space is a $T_1$ (Fréchet) space.

Hence the result, by definition of a fully normal space.

$\blacksquare$