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Point-finite collection

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In mathematics, a collection or family of subsets of a topological space is said to be point-finite if every point of lies in only finitely many members of [1][2]

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.[2]

References

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  1. ^ Willard 2004, p. 145–152.
  2. ^ a b Willard, Stephen (2012), General Topology, Dover Books on Mathematics, Courier Dover Publications, pp. 145–152, ISBN 9780486131788, OCLC 829161886.

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