Definition:Stone Space

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Let $B$ be a Boolean algebra.

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

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


$U$ 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.