Metric Space is Fully Normal

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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 $T_1$ (Fr├ęchet) space.

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

$\blacksquare$


Sources