# Nagata-Smirnov Metrization Theorem

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## Theorem

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

Then $T$ is metrizable if and only if $T$ is regular and has a basis that is countably locally finite.

## Proof

## Source of Name

This entry was named for Jun-iti Nagata and Yurii Mikhailovich Smirnov.

## Sources

- 1975: James R. Munkres:
*Topology*