Results 1 to 10 of about 275 (133)
Priestley duality for MV-algebras and beyond [PDF]
Forum Mathematicum, 2021 AbstractWe provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces.
Wesley Fussner +2 more
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Deriving Dualities in Pointfree Topology from Priestley Duality
Applied Categorical Structures, 2023 There are several prominent duality results in pointfree topology. The Hofmann-Lawson duality establishes that the category of continuous frames is dually equivalent to the category of locally compact sober spaces. This restricts to a dual equivalence between the categories of stably continuous frames and stably locally compact spaces, which further ...
G Bezhanishvili, Bezhanishvili G
exaly +5 more sources
Priestley Duality for Bilattices [PDF]
Studia Logica, 2012 We develop a Priestley-style duality theory for different classes of algebras having a bilattice reduct. A similar investigation has already been realized by B. Mobasher, D. Pigozzi, G. Slutzki and G. Voutsadakis, but only from an abstract category-theoretic point of view.
Umberto Rivieccio
exaly +6 more sources
Priestley Duality for Strong Proximity Lattices
Electronic Notes in Theoretical Computer Science, 2006 AbstractIn 1937 Marshall Stone extended his celebrated representation theorem for Boolean algebras to distributive lattices. In modern terminology, the representing topological spaces are zero-dimensional stably compact, but typically not Hausdorff. In 1970, Hilary Priestley realised that Stone's topology could be enriched to yield order-disconnected ...
Mohamed A El-Zawawy, Achim Jung
exaly +3 more sources
Priestley Duality and Representations of Global Dynamics
Qualitative Theory of Dynamical SystemsAbstract Asymptotic global dynamics is fundamentally an order structure. This relationship is naturally characterized in terms of a Priestley space derived from the attractors of a system, which provides an order-theoretic framework for the study of global dynamics.
William D Kalies, Robert Vandervorst
exaly +5 more sources
Algebraic frames in Priestley duality
Algebra Universalis23 pages, 6 figures, 6 ...
Guram Bezhanishvili +1 more
exaly +4 more sources
Natural and restricted Priestley duality for ternary algebras and their cousins [PDF]
Categories and General Algebraic Structures with Applications, 2022 Up to term equivalence, there are three ways to assign a nonemptyset C of constants to the three-element Kleene lattice, leading toternary algebras (C = {0, d, 1}), Kleene algebras (C = {0, 1}), and don’tknow algebras (C = {d}).
Brian Davey, Stacey Mendan
doaj +3 more sources
Duality theory for enriched Priestley spaces [PDF]
Journal of Pure and Applied Algebra, 2023 The term Stone-type duality often refers to a dual equivalence between a category of lattices or other partially ordered structures on one side and a category of topological structures on the other. This paper is part of a larger endeavour that aims to extend a web of Stone-type dualities from ordered to metric structures and, more generally, to ...
Hofmann, Dirk, Nora, Pedro
openaire +4 more sources
A non-commutative Priestley duality [PDF]
Topology and Its Applications, 2013 We prove that the category of left-handed strongly distributive skew lattices with zero and proper homomorphisms is dually equivalent to a category of sheaves over local Priestley spaces. Our result thus provides a non-commutative version of classical Priestley duality for distributive lattices and generalizes the recent development of Stone duality ...
Andrej Bauer +2 more
exaly +4 more sources
Journal of Pure and Applied Algebra, 1997 What is proved here is actually not a duality but a (covariant) equivalence: that between the localic analogues of the category of ordered Stone spaces (which were introduced by \textit{H. A. Priestley} in 1970 as the duals of distributive lattices) and of the category of coherent spaces (the non-Hausdorff generalization of Stone spaces which appeared ...
Townsend, Chris
core +4 more sources