# Nagata-Smirnov Metrization Theorem

## Theorem

Let $T = \struct {S, \tau}$ be a topological space.

Then:

$T$ is metrizable if and only if $T$ is regular and has a basis that is $\sigma$-locally finite.

## Source of Name

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