# 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.

 Title point-finite Canonical name Pointfinite Date of creation 2013-03-22 16:17:02 Last modified on 2013-03-22 16:17:02 Owner yark (2760) Last modified by yark (2760) Numerical id 5 Author yark (2760) Entry type Definition Classification msc 54A99 Synonym point finite Related topic LocallyFinite Related topic Metacompact Defines point finite collection Defines point-finite collection Defines point finiteness Defines point-finiteness