Stone space: Difference between revisions
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}}</ref> Such spaces are also called ''profinite'' spaces.<ref>{{nlab|id=Stone+space|title=Stone space}}</ref> They are named after [[Marshall Harvey Stone]]. |
}}</ref> Such spaces are also called ''profinite'' spaces.<ref>{{nlab|id=Stone+space|title=Stone space}}</ref> They are named after [[Marshall Harvey Stone]]. |
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A form of [[Stone's representation theorem for Boolean algebras]] states that every [[Boolean algebra]] is isomorphic to the algebra of [[clopen set]]s of a Stone space |
A form of [[Stone's representation theorem for Boolean algebras]] states that every [[Boolean algebra]] is isomorphic to the algebra of [[clopen set]]s of a Stone space. This isomorphism forms a [[dual category|category-theoretic duality]] between the categories of Boolean algebras and Stone spaces. |
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==References== |
==References== |
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Revision as of 01:23, 15 March 2017
In topology, and related areas of mathematics, a Stone space is a compact totally disconnected Hausdorff space.[1] Such spaces are also called profinite spaces.[2] They are named after Marshall Harvey Stone.
A form of Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to the algebra of clopen sets of a Stone space. This isomorphism forms a category-theoretic duality between the categories of Boolean algebras and Stone spaces.
References
- ^ "Stone space", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
- ^ Stone space at the nLab