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point finite (Definition)

A collection $ \mathcal{U}$ of subsets of a topological space $ X$ is said to be point finite if every point of $ X$ lies in only finitely many members of $ \mathcal{U}$.

Compare this to the stronger property of being locally finite.

Point-finiteness is used in the definition of metacompactness.



"point finite" is owned by yark.
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See Also: locally finite collection, metacompact

Other names:  point-finite
Also defines:  point finite collection, point-finite collection, point finiteness, point-finiteness
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Cross-references: metacompactness, locally finite, property, point, topological space, subsets, collection
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This is version 1 of point finite, born on 2006-09-27.
Object id is 8398, canonical name is PointFinite.
Accessed 1988 times total.

Classification:
AMS MSC: 54A99 (General topology :: Generalities :: Miscellaneous)
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