Definition:Locally Metrizable Space
Jump to navigation
Jump to search
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