# Locally metrizable space

From Topospaces

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

This is a variation of metrizability. View other variations of metrizability

## Definition

A topological space is termed **locally metrizable** if it satisfies the following equivalent conditions:

- Every point has an open neighbourhood which is a metrizable space
- Given a point, and any open neighbourhood of the point, there is a smaller open neighbourhood of the point which is metrizable