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 $pro(FinSet)$ of pro-objects in FinSet and finite sets sit $FinSet\hookrightarrow pro(FinSet)$ as finite discrete spaces. This is especially common when talking about profinite groups and related topics.

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)