# 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.