nLab
Stonean 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

Contents

Definition

A Stonean space is a compact, Hausdorff extremally disconnected topological space. Stonean spaces form a category if we take continuous open maps as morphisms.

Thus, the category of Stonean spaces is a (nonfull) subcategory of the category of Stone spaces and continuous maps.

As a consequence of Stone duality, the category of Stonean spaces is contravariantly equivalent to the category of complete Boolean algebras and continuous homomorphisms.

References

A standard textbook is

Last revised on April 29, 2019 at 14:09:01. See the history of this page for a list of all contributions to it.