nLab
stably compact space

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

(0,1)(0,1)-Category theory

Contents

Idea

Stably compact spaces are topological spaces which share many of the desirable properties of compact Hausdorff spaces, such as compactness and local compactness, without being Hausdorff or even T1.

They are also a convenient setting for convergence in an ordered setting, being deeply linked to compact ordered spaces.

Definition

A topological space XX is called stably compact if the following conditions are met:

Note that the latter notion of coherence is slightly different than the one given at coherent space.

Connection with compact ordered spaces

(…)

References

Created on October 21, 2019 at 12:59:36. See the history of this page for a list of all contributions to it.