Point-finite collection
From Infogalactic: the planetary knowledge core
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
This article incorporates material from point finite on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
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