nLab separable metric space

Redirected from "separable metric spaces".
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

Idea

In topology, a separable metric space is a topological space that is both separable and metrizable.

Properties

Dimension

Proposition

For separable metric spaces, the following notions of dimension all (exist and) coincide and are thus uniformly referred to as the dimension of a separable metric space:

  1. small and large inductive dimension;

  2. covering dimension.

(e.g. Engelking 78, Theorem 1.7.7)

References

Last revised on August 29, 2024 at 20:06:16. See the history of this page for a list of all contributions to it.