A completion for partially ordered abelian groups.
A completion functor for Cauchy groups.
A computation of positive one-peak posets that are Tits-sincere
A complete list of positive Tits-sincere one-peak posets is provided by applying combinatorial algorithms and computer calculations using Maple and Python. The problem whether any square integer matrix is ℤ-congruent to its transpose is also discussed. An affirmative answer is given for the incidence matrices and the Tits matrices of positive one-peak posets I.
A construction of mirror -algebras.
A construction of tolerances on modular lattices
A constructive characterization of the lattices of all retractions, preclosure, quasi-closure and closure operators on a complete lattice
A constructive “Closed subgroup theorem” for localic groups and groupoids
A constructive proof that every 3-generated l-group is ultrasimplicial
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 continuous geometry as a mathematical model for quantum mechanics
A continuous lattice L with DID(L) incomplete.
A continuum of totally incomparable hereditarily indecomposable Banach spaces
A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.
A contour view on uninorm properties
Any given increasing 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 convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube
We compare the forcing-related properties of a complete Boolean algebra with the properties of the convergences (the algebraic convergence) and on generalizing the convergence on the Cantor and Aleksandrov cube, respectively. In particular, we show that is a topological convergence iff forcing by does not produce new reals and that is weakly topological if satisfies condition (implied by the -cc). On the other hand, if is a weakly topological convergence, then is a -cc algebra...
A counterexample to a Kurepa's conjecture
A counterexample to a result concerning closure operators.
A decomposition of homomorphic images of nearlattices
By a nearlattice is meant a join-semilattice where every principal filter is a lattice with respect to the induced order. The aim of our paper is to show for which nearlattice and its element the mapping is a (surjective, injective) homomorphism of into .
A directed -group that is not a group of divisibility
A dual space characterization of - and -lattices of order ω+
A duality between algebras of basic logic and bounded representable -monoids
-algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that -algebras are the duals of bounded representable -monoids. This duality enables us to describe some structure properties of -algebras.
A duality between unary algebras and their subuniverse lattices