-posets
Darstellungen und Erweiterungen geordneter Mengen. I.
Darstellungen und Erweiterungen geordneter Mengen. II.
Decomposition of topologies on lattices and hyperspaces [Book]
Decompositions of directed sets with zero
Dedekind completions of lattices by ends
Definition of Flat Poset and Existence Theorems for Recursive Call
This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge. To achieve this...
Definitions of finiteness based on order properties
A definition of finiteness is a set-theoretical property of a set that, if the Axiom of Choice (AC) is assumed, is equivalent to stating that the set is finite; several such definitions have been studied over the years. In this article we introduce a framework for generating definitions of finiteness in a systematical way: basic definitions are obtained from properties of certain classes of binary relations, and further definitions are obtained from the basic ones by closing them under subsets...
Definizione dei clan binari e loro classificazione
L’albero binario (libero) è una struttura analoga a quella dei numeri naturali (standard), salvo che ci sono due operazioni di successivo. Nello studio degli alberi binari non standard, si ha bisogno di strutture ordinate che stiano a quella di albero binario libero come la struttura (ordinata) Z sta ad N. Si introducono perciò i clan binari e se ne studiano le classi di isomorfismo. Si dimostra che esse sono determinate dalle classi di similitudine delle successioni numerabili di 2 elementi, avendo...
Deformation of chains via a local symmetric group action.
Dénombrement des quasi-ordres sur un ensemble fini
Dense extensions of a partially ordered set.
Dense subsets of ordered sets
Some modifications of the definition of density of subsets in ordered (= partially ordered) sets are given and the corresponding concepts are compared.
Description combinatoire des ultramétriques
Destroying precaliber : an application of a Δ-systems lemma for closed sets
Determinants of matrices associated with incidence functions on posets
Let be a finite subset of a partially ordered set . Let be an incidence function of . Let denote the matrix having evaluated at the meet of and as its -entry and denote the matrix having evaluated at the join of and as its -entry. The set is said to be meet-closed if for all . In this paper we get explicit combinatorial formulas for the determinants of matrices and on any meet-closed set . We also obtain necessary and sufficient conditions for the matrices...
Determining c₀ in C(𝒦) spaces
For a countable compact metric space and a seminormalized weakly null sequence (fₙ)ₙ in C() we provide some upper bounds for the norm of the vectors in the linear span of a subsequence of (fₙ)ₙ. These bounds depend on the complexity of and also on the sequence (fₙ)ₙ itself. Moreover, we introduce the class of c₀-hierarchies. We prove that for every α < ω₁, every normalized weakly null sequence (fₙ)ₙ in and every c₀-hierarchy generated by (fₙ)ₙ, there exists β ≤ α such that a sequence of β-blocks...
Die Abgeschlossenheit der lexikographischen Summe in der Klasse distributiver Verbände
Die Abgeschlossenheit der lexikographischen Summe in der Klasse modularer Verbände
Die arithmetische Operation der Summe