Completely metrizable space: Difference between revisions

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==Relation with other properties==
==Relation with other properties==


===Stronger properties===
* [[Compact space|compact]] [[metrizable space]]
===Weaker properties===
===Weaker properties===


* [[Baire space]]
* [[Baire space]]

Latest revision as of 19:41, 11 May 2008

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

Weaker properties