Stone Space

A Stone space is a compact, Hausdorff, totally disconnected topological space that arises as the space of ultrafilters of a Boolean algebra or, in model theory, as the space of complete n-types (type space) equipped with the topology generated by sets of types containing a given formula; points correspond to ultrafilters/complete types and clopen sets correspond to syntactic Boolean combinations o

A compact, Hausdorff, zero-dimensional (totally disconnected) topological space that arises as the dual object of a Boolean algebra under Stone duality; points correspond to ultrafilters and clopen sets correspond to algebra elements.