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.

Relation with other properties

Stronger properties

Weaker properties