# Smirnov Metrization Theorem

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## Contents

## Theorem

Let $T = \left({S, \tau}\right)$ be a topological space.

Then $T$ is metrizable if and only if it is paracompact and locally metrizable.

## Proof

## Source of Name

This entry was named for Yurii Mikhailovich Smirnov.

## Sources

- 1975: James R. Munkres:
*Topology*