## You are here

Homepoint-finite

## Primary tabs

# point-finite

A collection $\mathcal{U}$ 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 $\mathcal{U}$.

Compare this to the stronger property of being locally finite.

Point-finiteness is used in the definition of metacompactness.

Defines:

point finite collection, point-finite collection, point finiteness, point-finiteness

Related:

LocallyFinite, Metacompact

Synonym:

point finite

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

54A99*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff

## Recent Activity

Sep 14

new problem: Geometry by parag

Aug 24

new question: Scheduling Algorithm by ncovella

new question: Scheduling Algorithm by ncovella

new problem: Geometry by parag

Aug 24

new question: Scheduling Algorithm by ncovella

new question: Scheduling Algorithm by ncovella