Completely metrizable space

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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


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

Weaker properties