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Statisch pairs in atomistic posets

Alireza Vaezi, Vilas Kharat (2017)

Mathematica Bohemica

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...

Subdirectly irreducible sectionally pseudocomplemented semilattices

Radomír Halaš, Jan Kühr (2007)

Czechoslovak Mathematical Journal

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...

Supremum properties of Galois-type connections

Árpád Száz (2006)

Commentationes Mathematicae Universitatis Carolinae

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 f of one preordered set X into another Y has been called (1) increasingly   g -normal, for some function g of Y into X , if for any x ∈ X and y ∈ Y we have f ( x ) ≤ y if and only if x ≤ g ( y ) ; (2) increasingly ϕ -regular, for some function ϕ of X into itself,...

Sur la caractérisation topologique des compacts à l'aide des demi-treillis des pseudométriques continues

Taras Banakh (1995)

Studia Mathematica

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

Bruno Leclerc (1990)

Mathématiques et Sciences Humaines

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).

Sur les prémeilleurordres

Maurice Pouzet (1972)

Annales de l'institut Fourier

Cet article traite de certains préordres généralisant le bon ordre. On étudie les rapports entre la notion de préordre artinien d’incomparabilité finie (pour qui toute partie a des éléments minimaux incomparables en nombre fini) et deux notions de prémeilleur ordre introduites successivement par Hash-Williams en 1965 puis par Jullien en 1969. On montre que ces deux notions sont identiques (ce qui était conjecturé par Jullien) au moyen du résultant suivant :Un préordre X est un prémeilleur ordre...

Symmetric difference on orthomodular lattices and Z 2 -valued states

Milan Matoušek, Pavel Pták (2009)

Commentationes Mathematicae Universitatis Carolinae

The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of Z 2 -valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space.

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