Wikipedia:
point finite collection
In mathematics, a collection 
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
.
Compare this to the stronger property of being locally finite.
Point-finiteness is used in the definition of a metacompact space.
This article incorporates material from point finite on PlanetMath, which is licensed under the GFDL.
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