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# 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*

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new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

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new image: information-theoretic-distributed-measurement-2.1 by rspuzio

Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia