Strongly paracompact space: Difference between revisions
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==Definition== | ==Definition== | ||
A [[topological space]] is said to be '''strongly paracompact''' if it satisfies the following condition: every open [[cover]] has a [[star-finite collection|star-finite]] open [[refinement]]. | A [[topological space]] is said to be '''strongly paracompact''' or '''fully normal''' if it satisfies the following condition: every open [[cover]] has a [[star-finite collection|star-finite]] open [[refinement]]. | ||
==Formalisms== | ==Formalisms== | ||
Revision as of 08:10, 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 strongly paracompact or fully normal if it satisfies the following condition: every open cover has a star-finite open refinement.
Formalisms
Refinement formalism
In the refinement formalism, the property of being strongly paracompact has the following refinement formal expression:
Open Star-finite open
In other words, every open cover can be refined to a star-finite open cover.