Nagata-Smirnov Metrization Theorem

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Theorem

Let $T = \left({S, \tau}\right)$ be a topological space.


Then $T$ is metrizable if and only if $T$ is regular and has a basis that is countably locally finite.


Proof


Source of Name

This entry was named for Jun-iti Nagata and Yurii Mikhailovich Smirnov.


Sources