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