# nLab Nagata-Smirnov metrization theorem

## Idea

The Nagata-Smirnov metrization theorem gives a necessary and sufficient condition under which a space is metrisable.

## Statement

###### Theorem

A topological space $X$ is metrisable if and only if it is regular, Hausdorff and has a countably locally finite base.

## References

Last revised on April 5, 2019 at 11:29:27. See the history of this page for a list of all contributions to it.