Results 221 to 230 of about 539 (243)

Dualities between complete lattices

Optimization, 1990
We study dualities between two complete lattices Eand Fi.e., mappings △:E→ F satisfying for all {x i } ieI ⊆E and all index sets I including the empty set I = O. We give characterizations and representations of dualities △, and some results on the dual △* F→Eof △ and on the associated hull operator △*△:E→Ein the general case and in various particular ...
J.E. Martinez-Legaz, I. Singer
openaire   +1 more source

Priestley duality for some subalgebra lattices

Studia Logica, 1996
The author characterizes Heyting algebras with a modular congruence lattice. His investigations are carried out within the Priestley space \(X\) of such algebras. The author also looks at Heyting algebras with complemented congruence or subalgebra lattices. For example, for finite Heyting spaces \(X\), \(\text{Con} (X)\) is complemented if and only if \
openaire   +2 more sources

Free Modal Lattices via Priestley Duality

Studia Logica, 2002
A modal lattice \(L\) is an algebra \(L=(L;\vee, \wedge,j,0, 1)\), where \((L;\vee, \wedge,0,1)\) is a bounded distributive lattice and \(j\) is a unary operation satisfying the following identities: (i) \(x\leq j(x)\), (ii) \(j(x)= j(j(x))\) and (iii) \(j(x\wedge y)=j(x) \wedge j(y)\).
openaire   +1 more source

A simplified duality for implicative lattices and l-groups

Studia Logica, 1996
A distributive lattice is an implicative lattice if besides the usual lattice-theoretic operations of meet and join, an auxiliary operation, the implication \(\to\), is given which is subject to equational conditions, like \(x\to (y\wedge y')= (x\to y)\wedge(x\to y')\), that generalize in an obvious way the Boolean case where \(x\to y=\neg x\vee y ...
openaire   +1 more source

Duality in Lattice Implication Algebra

2011
According to the general form of principle of duality in the sense of class [1], this paper tries to study the dual operators of operators in lattice implication algebra [2], especially the dual operator of implication operator and gives the expression of principle of duality in lattice implication algebra.
Li Zhao, Yang Xu
openaire   +1 more source

Atomistic Symmetric Lattices with Duality

1970
A lattice L with 0 and 1 is called a DAC-lattice when both L and its dual L* are AC-lattices, that is, atomistic lattices with the covering property. If L is a DAC-lattice then so is L* evidently.
Fumitomo Maeda, Shûichirô Maeda
openaire   +1 more source

On the duality of Dunford-Pettis operators on Banach lattices

Czechoslovak Mathematical Journal
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aqzzouz, Belmesnaoui, Elbour, Aziz, Aboutafail, Othman   +2 more
openaire   +1 more source

Choice-free topological duality for implicative lattices and Heyting algebras

Algebra Universalis, 2023
Chrysafis Hartonas, Hartonas Chrysafis
exaly  

Topological Duality for Distributive Lattices

Introducing Stone–Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area.
Gehrke, Mai, van Gool, Sam
openaire   +1 more source

Modules with fusion and implication based over distributive lattices: Representation and duality

Mathematica Slovaca, 2022
Ismael Calomino
exaly