Definition:Stone Space

Definition

Let $B$ be a Boolean algebra.

The Stone space of $B$ is the topological space:

$\map S B = \struct {U, \tau}$

where:

$U$ is the set of ultrafilters in $B$

$\tau$ is the topology generated by the basis consisting of all sets of the form:

$\set {x \in \map S B: b \in x}$

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.

Source of Name

This entry was named for Marshall Harvey Stone.