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

• Results about Stone spaces can be found here.