Completely metrizable space: Difference between revisions
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==Definition== | ==Definition== | ||
A [[topological space]] is said to be '''completely metrizable''' if it arises as the topological space of a [[complete metric space]], viz a metric space in which every Cauchy sequence converges. | 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== | ==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.