Point finite collection

In mathematics, a collection U of subsets of a topological space X is said to be point finite or a point finite collection if every point of X lies in only finitely many members of U .

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 metacompact.