Smirnov metrization theorem

This article is about a metrization theorem: a theorem that gives necessary and sufficient conditions for a metric (possibly with additional restrictions) to exist. In particular, it gives some conditions under which a topological space is metrizable.

Statement

A topological space is metrizable iff it is paracompact Hausdorff and locally metrizable.

Related results

• Nagata-Smirnov metrization theorem