Definition:Stone Space
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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
- Results about Stone spaces can be found here.
Source of Name
This entry was named for Marshall Harvey Stone.