Locally metrizable space

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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


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