# Point-finite collection

In mathematics, a collection of subsets of a topological space is said to be **point finite** or a **point finite collection** if every point of lies in only finitely many members of .^{[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

- 1 2 Willard, Stephen (2012),
*General Topology*, Dover Books on Mathematics, Courier Dover Publications, pp. 145–152, ISBN 9780486131788.

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