Point-finite collection

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In mathematics, a collection \mathcal{U} of subsets of a topological space X is said to be point finite or a point finite collection if every point of X lies in only finitely many members of \mathcal{U}.[1]

A topological space in which every open cover admits a point-finite open refinement is called metacompact. 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 paracompact. Every paracompact space is metacompact.[1]

References[edit]

  1. ^ a b Willard, Stephen (2012), General Topology, Dover Books on Mathematics, Courier Dover Publications, pp. 145–152, ISBN 9780486131788 .


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