nLab
metric spaces are fully normal

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

Statement

Every metric space, regarded as a topological space via its metric topology, is a fully normal topological space.

Applications

Together with Stone’s theorem that fully normal spaces are equivalently paracompact this implies that metric spaces are paracompact.

References

Last revised on August 29, 2018 at 15:18:32. See the history of this page for a list of all contributions to it.