Completely metrizable space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

Definition

A topological space is said to be completely metrizable (sometimes, topologically complete) if it arises as the topological space of a complete metric space, viz a metric space in which every Cauchy sequence converges.

Relation with other properties

Stronger properties

• compact metrizable space

Weaker properties

• Baire space