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.
Vincenzo Marra +2 more
exaly +10 more sources
Deriving Dualities in Pointfree Topology from Priestley Duality [PDF]
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 ...
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 +8 more sources
Priestley Duality for Strong Proximity Lattices [PDF]
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 [PDF]
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 Kalies, Robert Vandervorst
exaly +5 more sources
Algebraic frames in Priestley duality [PDF]
Algebra Universalis23 pages, 6 figures, 6 ...
Bezhanishvili Guram +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
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 ...
Samuel Jacob van Gool +2 more
exaly +4 more sources
Open Mathematics, 2006 The authors investigate a topological representation for some algebraic structures of fuzzy logic using the results given in [\textit{S. A. Celani}, ``Bounded distributive lattices with fusion and implication'', Southeast Asian Bull. Math. 28, 999--1010 (2004; Zbl 1065.03050)].
Cabrer Leonardo, Celani Sergio
doaj +3 more sources
Expanding Belnap 2: the dual category in depth [PDF]
Categories and General Algebraic Structures with Applications, 2022 Bilattices, which provide an algebraic tool for simultaneously modelling knowledge and truth, were introduced by N.D. Belnap in a 1977 paper entitled How a computer should think.
Andrew Craig +2 more
doaj +1 more source