# Difference between revisions of "Nagata-Smirnov Metrization Theorem"

The Nagata-Smirnov Metrization Theorem gives a full characterization of metrizable topological spaces.[1] Essentially, the Nagata-Smirnov Metrization Theorem states that the regularity of a space $X$ and the existence of a countably locally finite basis for $X$ are equivalent to metrizability of $X$.
A topological space $X$ is metrizable if and only if $X$ is regular and has a basis that is countably locally finite.[2]