nLab
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 subset {S iX} iI\{S_i \subset X\}_{i \in I} is locally discrete if every point xXx \in X has a neighborhood which intersects at most one of the S iS_i.

Often one can find a base of a topological space that decomposes into a countable union of locally discrete sets. In this case the base is called σ \sigma -discrete. Such a base can be found for any metric space.

References

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

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

Last revised on April 10, 2019 at 04:18:20. See the history of this page for a list of all contributions to it.