nLab
Stone space

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)