# Bing metrization theorem

In topology, the Bing metrization theorem, named after R. H. Bing, characterizes when a topological space is metrizable. The theorem states that a topological space $X$ is metrizable if and only if it is regular and T0 and has a σ-discrete basis. A family of sets is called σ-discrete when it is a union of countably many discrete collections, where a family $F$ of subsets of a space $X$ is called discrete, when every point of $X$ has a neighborhood that intersects at most one member of $F$.