Metric Space is Paracompact

Theorem

Let $M = \left({A, d}\right)$ be a metric space.

Then $M$ is a paracompact space.

Proof

We have that a Metric Space is Fully Normal.

Then we have that a Fully Normal Space is Paracompact.

$\blacksquare$

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 5$