Definition:Stone Space

Definition
Let $B$ be a Boolean algebra.

The Stone space of $B$ is the topological space:
 * $S \left({B}\right) = \left({U, \tau}\right)$

where:
 * $U$ is the set of ultrafilters in $B$
 * $\tau$ is the topology generated by the basis consisting of all sets of the form:
 * $\left\{{x \in S \left({B}\right): b \in x}\right\}$
 * for some $b \in B$.

Also see

 * Stone Space is Topological Space


 * Stone's Representation Theorem for Boolean Algebras