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Point-finite

In mathematics, a collection or familyU{\displaystyle {\mathcal {U}}} of subsets of a topological spaceX{\displaystyle X} is said to be point-finite if every point of X{\displaystyle X} lies in only finitely many members of U.{\displaystyle {\mathcal {U}}.}A metacompact space is a topological space in which every open cover admits a point-finite open refinement.

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