Results 11 to 20 of about 1,649 (263)
CHOICE-FREE STONE DUALITY [PDF]
The Journal of Symbolic Logic, 2019 AbstractThe standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras.
Nick Bezhanishvili, Wesley H. Holliday
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A general Stone-Gel’fand duality [PDF]
Transactions of the American Mathematical Society, 1979 We give a simple characterization of full subcategories of equational categories. If a \mathcal {a}
Lambek, J., Rattray, B. A.
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A NONCOMMUTATIVE GENERALIZATION OF STONE DUALITY [PDF]
Journal of the Australian Mathematical Society, 2010 AbstractWe prove that the category of boolean inverse monoids is dually equivalent to the category of boolean groupoids. This generalizes the classical Stone duality between boolean algebras and boolean spaces. As an instance of this duality, we show that the boolean inverse monoid Cn associated with the Cuntz groupoid Gn is the strong orthogonal ...
Lawson, M. V.
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Topology and its Applications, 2004 Stone duality, the duality between Boolean algebras and Boolean spaces, has encountered many modifications, and then attempts for a unified treatment of those. The present paper is another such attempt, based on a careful analysis of the relation between the categories of complete join-semilattices and complete meet-semilattices, respectively. The main
Erné, Marcel
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Stone duality for spectral sheaves and the patch monad
Journal of Pure and Applied Algebra, 2023 We establish a duality between global sheaves on spectral spaces and right distributive bands. This is a sheaf-theoretical extension of classical Stone duality between spectral spaces and bounded distributive lattices. The topology of a spectral space admits a refinement, the so-called patch topology, giving rise to a patch monad on sheaves over a ...
Berger, Clemens, Gehrke, Mai
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Stone duality, topological algebra, and recognition [PDF]
Journal of Pure and Applied Algebra, 2016 Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion of any abstract algebra is the extended Stone dual space of the Boolean algebra of recognizable subsets of the ...
Gehrke, Mai
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Stone Duality and the Substitution Principle. [PDF]
26th EACSL Annual Conference on Computer Science Logic (CSL 2017), 2017 In this paper we relate two generalisations of the finite monoid recognisers of automata theory for the study of circuit complexity classes: Boolean spaces with internal monoids and typed monoids. Using the setting of stamps, this allows us to generalise a number of results from algebraic automata theory as it relates to Büchi's logic on words.
Célia Borlido +3 more
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A Stone-type duality for semilattices with adjunctions
Journal of Logic and ComputationAbstract This paper focuses on semilattices with adjunctions (SLatas), which are semilattices with a greatest element enriched with a pair of adjoint maps. We develop a spectral-style duality for SLatas, building on prior topological dualities for monotone semilattices. As an application of this duality, we characterize SLata congruences
Belén Gimenez +2 more
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Stone duality for lattice expansions
Logic Journal of the IGPL, 2018 Chrysafis Hartonas, Hartonas Chrysafis
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, 2023 We show how Stone duality can be extended from maps to relations. This is achieved by working order enriched and defining a relation from A to B as both an order-preserving function from the opposite of A times B to the 2-element chain and as a subobject of A times B. We show that dual adjunctions and equivalences between regular categories, taken in a
Alexander Kurz 0001 +2 more
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