Connecting fuzzifying topologies and generalized ideals by means of fuzzy preorders.
Connection between set theory and the fixed point property
Construction du treillis de Galois d'une relation binaire
Cet article constitue une présentation unifiée des principales méthodes de construction du treillis de Galois d'une correspondance. Nous rappelons d'abord sa définition, puis nous décrivons quatre algorithmes de construction des éléments du treillis qui sont les rectangles maximaux de la relation binaire. Ces algorithmes ne sont pas originaux. Les descriptions précises de algorithmes, le plus souvent absentes des publications originales, permettent une programmation simple, dans un langage procédural...
Contexts and sublattices of concept lattices
Continu expérimental et continu mathématique
Continuous posets and adjoint sequences.
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.
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...
Correction to the paper “Selfduality of the system of intervals of a partially ordered set”
Corrections à l'article "ordres C.A.C.", Fundamenta Mathematicae 79 (1973), pp. 11-22
Corrigendum: A completion for partially ordered abelian groups.
Corrigendum to "Perfect semilattices".
Countable 1-transitive coloured linear orderings II
This paper gives a structure theorem for the class of countable 1-transitive coloured linear orderings for a countably infinite colour set, concluding the work begun in [1]. There we gave a complete classification of these orders for finite colour sets, of which there are ℵ₁. For infinite colour sets, the details are considerably more complicated, but many features from [1] occur here too, in more marked form, principally the use (now essential it seems) of coding trees, as a means of describing...
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.
Countable homogeneous coloured partial orders [Book]
Counterexamples to the Neggers-Stanley conjecture.
Counting biorders.
Counting transitive relations.