Locally metrizable space

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

Relation with other properties

Stronger properties

• Metrizable space
• Locally Euclidean space