Chapitre II Chaînes d'idéaux d'un ensemble ordonné
Characteristic for reflexive relations.
Characterization of a full set of probabilities on some posets.
Characterization of all order relations in direct sums of ordered groups.
Characterization of distributive sets by generalized annihilators
Distributive ordered sets are characterized by so called generalized annihilators.
Characterization of lattices of convex subsets of posets
Characterization of posets of intervals
If is a class of partially ordered sets, let denote the system of all posets which are isomorphic to the system of all intervals of for some We give an algebraic characterization of elements of for being the class of all bounded posets and the class of all posets satisfying the condition that for each there exist a minimal element and a maximal element with respectively.
Characterizations of 0-distributive posets
The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.
Characterizations of certain classes of posets having Gs-lattices of a relatively small size
Characterizations of effective sets and nonexpansive multipliers in conditionally complete and infinitely distributive partially ordered sets.
Characterizations of nonexpansive multipliers on partially ordered sets
Characterizing triplets for modular pseudocomplemented ordered sets
Coloring digraphs by iterated antichains
We show that the minimum chromatic number of a product of two -chromatic graphs is either bounded by 9, or tends to infinity. The result is obtained by the study of coloring iterated adjoints of a digraph by iterated antichains of a poset.
Comments on the completeness of order complements and on the Prüfer numbers
Common fixed points and fixed edges for monotone mappings in posets
Compact partially ordered sets and compactification of partially ordered sets
Compactifications of partially ordered sets
Compactness properties of weighted summation operators on trees-the critical case
The aim of this paper is to provide upper bounds for the entropy numbers of summation operators on trees in a critical case. In a recent paper [Studia Math. 202 (2011)] we elaborated a framework of weighted summation operators on general trees where we related the entropy of the operator to those of the underlying tree equipped with an appropriate metric. However, the results were left incomplete in a critical case of the entropy behavior, because this case requires much more involved techniques....
Compactness properties of weighted summation operators on trees
We investigate compactness properties of weighted summation operators as mappings from ℓ₁(T) into for some q ∈ (1,∞). Those operators are defined by , t ∈ T, where T is a tree with partial order ⪯. Here α and σ are given weights on T. We introduce a metric d on T such that compactness properties of (T,d) imply two-sided estimates for , the (dyadic) entropy numbers of . The results are applied to concrete trees, e.g. moderately increasing, biased or binary trees and to weights with α(t)σ(t)...
Compatibility in orthomodular posets