Sortable elements for quivers with cycles.
Splitting numbers of grids.
Standard and nonstandard representability of positive uncertainty orderings
Axioms are given for positive comparative probabilities and plausibilities defined either on Boolean algebras or on arbitrary sets of events. These axioms allow to characterize binary relations representable by either standard or nonstandard measures (i. e. taking values either on the real field or on a hyperreal field). We also study relations between conditional events induced by preferences on conditional acts.
Standard completions for quasiordered sets.
Standard paths in another composition poset.
Stationary sets, trees and continuums.
Statisch pairs in atomistic posets
We introduce statisch pairs in atomistic posets and study its relationships with some known concepts in posets such as biatomic and dual modular pairs, perspectivity and subspaces of atom space of an atomistic poset. We generalize the notion of exchange property in posets and with the help of it we prove the equivalence of dual modular, biatomic and statisch pairs in atomistic posets. Also, we prove that the set of all finite elements of a statisch poset with such property forms an ideal. -relation...
Stone spaces of more partially ordered sets
Strengthened fixed point property and products in ordered sets
Strong elements in lattices
Structure de l'ensemble des fermetures d'un treillis complet
Subdirectly irreducible decomposition of some algebras having the semilattice structure
Subdirectly irreducible sectionally pseudocomplemented semilattices
Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented...
Subdirectly irreducible semilattices with an automorphism.
Subdirectly Irreducibles in some Varieties of Algebras having the Semilattice Structure
Sunflowers in lattices.
Supremum properties of Galois-type connections
In a former paper, motivated by a recent theory of relators (families of relations), we have investigated increasingly regular and normal functions of one preordered set into another instead of Galois connections and residuated mappings of partially ordered sets. A function of one preordered set into another has been called (1) increasingly -normal, for some function of into , if for any and we have if and only if ; (2) increasingly -regular, for some function of into itself,...
Sur des conjectures de R. Fraisse
Sur la caractérisation topologique des compacts à l'aide des demi-treillis des pseudométriques continues
For a Tikhonov space X we denote by Pc(X) the semilattice of all continuous pseudometrics on X. It is proved that compact Hausdorff spaces X and Y are homeomorphic if and only if there is a positive-homogeneous (or an additive) semi-lattice isomorphism T:Pc(X) → Pc(Y). A topology on Pc(X) is called admissible if it is intermediate between the compact-open and pointwise topologies on Pc(X). Another result states that Tikhonov spaces X and Y are homeomorphic if and only if there exists a positive-homogeneous...
Sur le nombre d'éléments des niveaux des produits de chaînes et des treillis permutoèdres
Les produits de chaînes comptent parmi les ensembles (partiellement) ordonnés les plus fréquemment rencontrés. On rappelle, avec des démonstrations en partie nouvelles, divers résultats exacts ou approchés sur les cardinaux de leurs niveaux et sur le nombre de ses niveaux de cardinal maximum. Un plongement avec de bonnes propriétés permet d'appliquer ces résultats aux niveaux du permutoèdre (ordre faible de Bruhat sur les permutations).