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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]}

- Willard, Stephen (2004) [1970].
*General Topology*. Mineola, N.Y.: Dover Publications. ISBN 978-0-486-43479-7. OCLC 115240. - Willard, Stephen (2012) [1970].
*General Topology*. Mineola, N.Y.: Courier Dover Publications. ISBN 9780486131788. OCLC 829161886.

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