# Nagata-Smirnov Metrization Theorem

 It has been suggested that this page or section be merged into Smirnov Metrization Theorem. (Discuss)

## 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.

## Source of Name

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