Definition:Stone Space/Boolean Lattice

Definition
Let $B$ be a Boolean lattice.

The Stone space of $B$ is the topological space:
 * $\map S B = \struct {U, \tau}$

where:
 * $(1): \quad U$ is the set of ultrafilters in $B$
 * $(2): \quad \tau$ is the topology generated by the basis consisting of all sets of the form:
 * $\exists b \in B: \set {x \in U: b \in x}$

Also see

 * Stone Space of Boolean Lattice is Topological Space
 * Stone Space of Boolean Lattice is Stone Space
 * Stone's Representation Theorem for Boolean Algebras