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In [[mathematics]], '''Stone's representation theorem for Boolean algebras''', named in honor of [[Marshall H. Stone]], is the [[duality of categories|duality]] between the [[category theory|category]] of [[Boolean algebra]]s and the category of '''Stone spaces''', i.e., [[totally disconnected]] [[Compact space|compact]] [[Hausdorff space|Hausdorff]] [[topological space]]s. It is a special case of [[Stone duality]], a general framework for dualities between topological spaces and partially ordered sets. In the category of Boolean algebras, the morphisms are Boolean homomorphisms. In the category of Stone spaces, the morphisms are continuous functions. Stone's duality generalises to infinite sets of propositions the use of [[truth table]]s to characterise elements of finite Boolean algebras. It employs systematically the two-element Boolean algebra {0,1} or {F,T} of truth-values, as the target of homomorphisms; this algebra may be written simply as 2.
In detail, the Stone space of a Boolean algebra ''A'' is the set of all 2-valued homomorphisms on ''A'', with the topology of [[pointwise convergence]] of [[net (mathematics)|nets]] of such homomorphisms.
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