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# point-finite

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.

Defines:

point finite collection, point-finite collection, point finiteness, point-finiteness

Related:

LocallyFinite, Metacompact

Synonym:

point finite

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

54A99*no label found*

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