nLab
countably 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 subsets {S iX} iI\{S_i \subset X\}_{i \in I} is countably locally finite or σ\sigma-locally finite if it is a countable union of locally finite sets of subsets.

This property is used in Nagata-Smirnov metrization theorem:

Theorem

A topological space X X is metrisable if and only if it is regular, Hausdorff and has a countably locally finite base.

References

Last revised on April 5, 2019 at 18:19:43. See the history of this page for a list of all contributions to it.