Point-finite collection

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Template:Short description In mathematics, a collection or family 𝒰 of subsets of a topological space X is said to be point-finite if every point of X lies in only finitely many members of 𝒰.Template:Sfn[1]

A metacompact space is a topological space in which every open cover admits a point-finite open refinement. Every locally finite collection of subsets of a topological space is also point-finite. A topological space in which every open cover admits a locally finite open refinement is called a paracompact space. Every paracompact space is therefore metacompact.[1]

Dieudonné's theorem

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The original proof uses Zorn's lemma, while Willard uses transfinite recursion.

References

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This article incorporates material from point finite on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

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