Bing's Metrization Theorem

From ProofWiki
Jump to navigation Jump to search


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


$T$ is metrizable if and only if $T$ is regular and has a $\sigma$-discrete basis


Source of Name

This entry was named for R.H. Bing.

Historical Note

Bing's Metrization Theorem was discovered in $1951$ by R.H. Bing, independently of the Nagata-Smirnov Metrization Theorem discovered by Jun-iti Nagata ($1950$) and Yurii Mikhailovich Smirnov ($1951$).

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