nLab
Stone space

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 space is a compact, Hausdorff totally disconnected topological space.

Stone spaces are sometimes called profinite spaces, since they are precisely the spaces which are small cofiltered limits of finite discrete spaces, and moreover (as a consequence of Stone duality) the category of Stone spaces is equivalent to the category pro(FinSet)pro(FinSet) of pro-objects in FinSet and finite sets sit FinSetpro(FinSet)FinSet\hookrightarrow pro(FinSet) as finite discrete spaces. This is especially common when talking about profinite groups and related topics.

References

A standard textbook is

See also

See also

  • S. B. Niefield, K.I. Rosenthal, Sheaves of integral domains on stone spaces, Journal of Pure and Applied Algebra Volume 47, Issue 2, August 1987, Pages 173–179

Revised on March 28, 2014 06:34:02 by Tim Porter (2.26.28.93)