Bing's Metrization Theorem

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

Then:


 * $T$ is metrizable $T$ is regular and $T_0$ and has a $\sigma$-discrete basis

Historical Note
The theorem by was discovered in $1951$ independently of the Nagata-Smirnov Metrization Theorem discovered by  ($1950$) and  ($1951$).

The two theorems are often merged as the Bing-Nagata-Smirnov Metrization Theorem.