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𝒵 -distributive function lattices

Marcel Erné (2013)

Mathematica Bohemica

It is known that for a nonempty topological space X and a nonsingleton complete lattice Y endowed with the Scott topology, the partially ordered set [ X , Y ] of all continuous functions from X into Y is a continuous lattice if and only if both Y and the open set lattice 𝒪 X are continuous lattices. This result extends to certain classes of 𝒵 -distributive lattices, where 𝒵 is a subset system replacing the system 𝒟 of all directed subsets (for which the 𝒟 -distributive complete lattices are just the continuous...

A characterization of commutative basic algebras

Ivan Chajda (2009)

Mathematica Bohemica

A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.

A class of multiplicative lattices

Tiberiu Dumitrescu, Mihai Epure (2021)

Czechoslovak Mathematical Journal

We study the multiplicative lattices L which satisfy the condition a = ( a : ( a : b ) ) ( a : b ) for all a , b ∈ L . Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group ℤ or ℝ . A sharp lattice L localized at its maximal elements are totally ordered sharp lattices. The converse is true if L has finite character.

A classification of rational languages by semilattice-ordered monoids

Libor Polák (2004)

Archivum Mathematicum

We prove here an Eilenberg type theorem: the so-called conjunctive varieties of rational languages correspond to the pseudovarieties of finite semilattice-ordered monoids. Taking complements of members of a conjunctive variety of languages we get a so-called disjunctive variety. We present here a non-trivial example of such a variety together with an equational characterization of the corresponding pseudovariety.

A constructive proof that every 3-generated l-group is ultrasimplicial

Daniele Mundici, Giovanni Panti (1999)

Banach Center Publications

We discuss the ultrasimplicial property of lattice-ordered abelian groups and their associated MV-algebras. We give a constructive proof of the fact that every lattice-ordered abelian group generated by three elements is ultrasimplicial.

A contour view on uninorm properties

Koen C. Maes, Bernard De Baets (2006)

Kybernetika

Any given increasing [ 0 , 1 ] 2 → [ 0 , 1 ] function is completely determined by its contour lines. In this paper we show how each individual uninorm property can be translated into a property of contour lines. In particular, we describe commutativity in terms of orthosymmetry and we link associativity to the portation law and the exchange principle. Contrapositivity and rotation invariance are used to characterize uninorms that have a continuous contour line.

A family of totally ordered groups with some special properties

Elena Olivos (2005)

Annales mathématiques Blaise Pascal

Let K be a field with a Krull valuation | | and value group G ≠ { 1 } , and let B K be the valuation ring. Theories about spaces of countable type and Hilbert-like spaces in [1] and spaces of continuous linear operators in [2] require that all absolutely convex subsets of the base field K should be countably generated as B K -modules.By [1] Prop. 1.4.1, the field K is metrizable if and only if the value group G has a cofinal sequence. We prove that for any fixed cardinality ℵ κ , there exists a metrizable field K ...

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