nLab
locally finite set of subsets

Contents

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Contents

Definition

Given a topological space XX, then a set of subset {S iX} iI\{S_i \subset X\}_{i \in I} is locally finite if every point xXx \in X intersects only a finite number of the S iS_i.

Often this property is considered for open covers, see at locally finite open cover. But the condition also plays a role for collections of subsets which are not open or not covering, for instance in Michael's theorem (Michael 53, theorem 1).

References

Last revised on April 5, 2019 at 18:21:09. See the history of this page for a list of all contributions to it.