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Minimal reducible bounds for hom-properties of graphs

Amelie Berger, Izak Broere (1999)

Discussiones Mathematicae Graph Theory

Let H be a fixed finite graph and let → H be a hom-property, i.e. the set of all graphs admitting a homomorphism into H. We extend the definition of → H to include certain infinite graphs H and then describe the minimal reducible bounds for → H in the lattice of additive hereditary properties and in the lattice of hereditary properties.

Modular functions on multilattices

Anna Avallone (2002)

Czechoslovak Mathematical Journal

We prove that every modular function on a multilattice L with values in a topological Abelian group generates a uniformity on L which makes the multilattice operations uniformly continuous with respect to the exponential uniformity on the power set of L .

Modularity and distributivity of the lattice of Σ -closed subsets of an algebraic structure

Ivan Chajda, Petr Emanovský (1995)

Mathematica Bohemica

Let 𝒜 = ( A , F , R ) be an algebraic structure of type τ and Σ a set of open formulas of the first order language L ( τ ) . The set C Σ ( 𝒜 ) of all subsets of A closed under Σ forms the so called lattice of Σ -closed subsets of 𝒜 . We prove various sufficient conditions under which the lattice C Σ ( 𝒜 ) is modular or distributive.

Natural extension of a congruence of a lattice to its lattice of convex sublattices

S. Parameshwara Bhatta, H. S. Ramananda (2011)

Archivum Mathematicum

Let L be a lattice. In this paper, corresponding to a given congruence relation Θ of L , a congruence relation Ψ Θ on C S ( L ) is defined and it is proved that 1. C S ( L / Θ ) is isomorphic to C S ( L ) / Ψ Θ ; 2. L / Θ and C S ( L ) / Ψ Θ are in the same equational class; 3. if Θ is representable in L , then so is Ψ Θ in C S ( L ) .

New constructions of uni-nullnorms on certain classes of bounded lattices by closure (interior) operators

Tao Wu (2024)

Kybernetika

The primary aim of this article is to put forward new classes of uni-nullnorms on certain classes of bounded lattices via closure (interior) operators. Due to the new classes of uninorms combining both a t-norm T and a t-conorm S by various kinds of closure operators or interior operators, the relationships and properties among the same class of uninorms on L , we obtain new classes of uni-nullnorms on L via closure (interior) operators. The constructions of uni-nullnorms on some certain classes...

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