Point-finite collection
In mathematics, a collection  formula_1 of subsets of a topological space formula_2 is said to be point-finite if every point of formula_2 lies in only finitely many members of formula_1. A topological space in which every open cover admits a point-finite open refinement is called metacompact. Every locally finite collection of subsets of a topological space is also point-finite. A topological space in which every open cover admits a locally finite open refinement is called paracompact. Every paracompact space is therefore metacompact.