Point-finite collection

In mathematics, a collection or family $$\mathcal{U}$$ 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 $$\mathcal{U}.$$

A metacompact space is a topological space in which every open cover admits a point-finite open refinement. 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 a paracompact space. Every paracompact space is therefore metacompact.