Continuity and Extension of Valuations
Continuity and Modularity of the Lattice of Closed Subspaces of a Locally Convex Space.
Continuity in partially ordered sets.
Continuous categories revisited.
Continuous lattices and compact Lawson semilattices.
Contributions to some generalizations of lattices
Control and separating points of modular functions
Convex automorphisms of a lattice
Convex independence and the structure of clone-free multipartite tournaments
We investigate the convex invariants associated with two-path convexity in clone-free multipartite tournaments. Specifically, we explore the relationship between the Helly number, Radon number and rank of such digraphs. The main result is a structural theorem that describes the arc relationships among certain vertices associated with vertices of a given convexly independent set. We use this to prove that the Helly number, Radon number, and rank coincide in any clone-free bipartite tournament. We...
Convex isomorphic ordered sets
V. I. Marmazejev introduced in [5] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which lattices are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim of this paper is to generalize this concept to ordered sets and to characterize convex isomorphic ordered sets in the general case of modular, distributive or complemented ordered...
Convex isomorphism of -lattices
V. I. Marmazejev introduced in [3] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which the lattice are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim this paper is to generalize this concept to the -lattices defined in [2] and to characterize the convex isomorphic -lattices.
Convex isomorphisms of directed multilattices
By applying the solution of the internal direct product decomposition we investigate the relations between convex isomorphisms and direct product decompositions of directed multilattices.
Convex subsets of partial monounary algebras
Convexity in subsets of lattices.
The notion of convex set for subsets of lattices in one particular case was introduced in [1], where it was used to study Paretto's principle in the theory of group choice. This notion is based on a betweenness relation due to Glivenko [2]. Betweenness is used very widely in lattice theory as basis for lattice geometry (see [3], and, especially [4 part 1]).In the present paper the relative notions of convexity are considered for subsets of an arbitrary lattice.In section 1 certain relative notions...
Corrections à l'article "ordres C.A.C.", Fundamenta Mathematicae 79 (1973), pp. 11-22
Corrigendum: A completion for partially ordered abelian groups.
Corrigendum à l'article "Sur la construction de certaines MS-algèbres" (Port. Math., 39(1-4) (1980), 489-496)
Corrigendum to "Perfect semilattices".
Countable chains of distributive lattices as maximal semilattice quotients of positive cones of dimension groups
We construct a countable chain of Boolean semilattices, with all inclusion maps preserving the join and the bounds, whose union cannot be represented as the maximal semilattice quotient of the positive cone of any dimension group. We also construct a similar example with a countable chain of strongly distributive bounded semilattices. This solves a problem of F. Wehrung.
Covering condition in the lattice of radical classes of linearly ordered groups