lies in only finitely many members of
[1][2] 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.
is normal if and only if each point-finite open cover of
is an open cover indexed by a set
The original proof uses Zorn's lemma, while Willard uses transfinite recursion.
This article incorporates material from point finite on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
This topology-related article is a stub.