nLab
Stone locale

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

Definition

A Stone locale is a compact zero-dimensional? locale.

Properties

In presence of the axiom of choice, every Stone locale is spatial? and the category of Stone locales is equivalent to the category of Stone spaces.

Stone duality

The Stone duality theorem states that the category of Stone locales is contravariantly equivalent to the category of Boolean algebras.

Unlike the corresponding statement for Stone spaces, this version is fully constructive and is valid in any W-topos.

In fact, the traditional Stone duality is an immediate consequence of the localic Stone duality and the spatiality of Stone locales.

References

Created on July 23, 2019 at 19:24:28. See the history of this page for a list of all contributions to it.