nLab
countably compact metric spaces are equivalently compact metric spaces

Context

Analysis

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

Let (X,d)(X,d) be a metric space, regarded as a topological space via its metric topology. Then the following are equivalent:

  1. (X,d)(X,d) is a countably compact topological space.

  2. (X,d)(X,d) is a compact topological space.

References

Created on April 14, 2017 at 12:40:12. See the history of this page for a list of all contributions to it.