nLab
countably locally discrete 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 discrete or σ\sigma-locally discrete if it is a countable union of locally discrete sets of subsets.

Note that open covers of metric spaces have open countably locally discrete refinements.

Example

References

  • Ryszard Engelking, General Topology, Heldermann Verlag Berlin, 1989.

  • K. Kuratowski, Topology, 2014, vol. 1.

Last revised on April 10, 2019 at 04:21:09. See the history of this page for a list of all contributions to it.