Definition:Stone Space
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Definition
Let $S$ be a topological space.
Let $S$ be:
Then $S$ is a Stone space.
Boolean Lattice
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
- Results about Stone spaces can be found here.
Source of Name
This entry was named for Marshall Harvey Stone.
Sources
- 1987: S.B. Niefield and K.I. Rosenthal: Sheaves of Integral Domains on Stone Spaces (J. Pure Appl. Algebra Vol. 47: pp. 173 – 179)
Zentralblatt MATH: 0631.13018