User:Leigh.Samphier/Topology/Nagata-Smirnov Metrization Theorem

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

Then:


 * $T$ is metrizable $T$ is regular and has a basis that is $\sigma$-locally finite.

Necessary Condition
Let $T$ be metrizable.

Sufficient Condition
Let $T$ be regular.

Let $T$ have a basis that is $\sigma$-locally finite.