Definition:Locally Metrizable Space

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Definition

Let $T = \struct {S, \tau}$ be a topological space.


The space $T$ is locally metrizable if and only if:

every point of $S$ is contained in an open set that is metrizable in the subspace topology.


Sources

  • 1975: James R. Munkres: Topology: Chapter $6$: Metrization Theorems and Paracompactness: $\S41$: The Smirnov Metrization Theorem