Smirnov Metrization Theorem

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Theorem

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


Then:

$T$ is metrizable if and only if $T$ is paracompact and locally metrizable.


Proof




Source of Name

This entry was named for Yurii Mikhailovich Smirnov.


Sources

  • 1975: James R. Munkres: Topology: Chapter $6$: Metrization Theorems and Paracompactness: $\S41$: The Smirnov Metrization Theorem: Theorem: $42.1$