nLab
metrisable topological space

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

A topological space (X,τ)(X,\tau) is called metrisable if there exists the stucture of a metric space (X,d)(X,d) on the underlying set, such that τ\tau is the corresponding metric topology.

Metrisability theorem

Various theorems state sufficient conditions for a topological space to be metrisable:

(…)

References

See also

Created on May 17, 2017 08:02:19 by Urs Schreiber (92.218.150.85)