Paracompact space: Difference between revisions
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==Definition== | ==Definition== | ||
A [[topological space]] is said to be '''paracompact''' if it satisfies the following condition: every open cover has a [[locally finite collection|locally finite]] open [[refinement]]. | A [[topological space]] is said to be '''paracompact''' if it satisfies the following condition: every open [[cover]] has a [[locally finite collection|locally finite]] open [[refinement]]. | ||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 06:18, 18 August 2007
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
This is a variation of compactness. View other variations of compactness
Definition
A topological space is said to be paracompact if it satisfies the following condition: every open cover has a locally finite open refinement.