Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of T0-spaces instead of restricting to posets. In this paper, we respond to this calling by proving a topological parallel of a 2005 result due to B. Zhao and D. Zhao, i.e., an order-theoretic characterisation of those posets for which the Scott-conve...

The $\Gamma$-colored $d$-complete posets correspond to certain Borel representations that are analogous minuscule of semisimple Lie algebras. We classify which specifies the structure associated representations. show finite precisely dominant heaps J.R. Stembridge. These reformulations and extensions colored R.A. Proctor. also connected infinite order filters full R.M. Green.

Let D be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On ZD we define a product and a coproduct, together with an internal product, that is, degree-preserving. With these operations ZD is a Hopf algebra, self-dual with respect to a scalar product which counts the number of pictures (in the sense of Zelevinsky) between two do...

Using countable support iterations of S -proper posets, we show that the existence of a ∆3 definable wellorder of the reals is consistent with each of the following: d < c, b < a = s, b < g.

Given a poset P , the set, Γ(P), of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Pos d (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P) ∼ = Γ(Q) implies P ∼ = Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Pos d is ...

Macaulay posets are posets for which there is an analogue of the classical KruskalKatona theorem for finite sets. These posets are of great importance in many branches of combinatorics and have numerous applications. We survey mostly new and also some old results on Macaulay posets. Emphasis is also put on construction of extremal ideals in Macaulay posets.

Abstract Generalized orthomodular posets were introduced recently by D. Fazio, A. Ledda and the first author of present paper in order to establish a useful tool for studying logic quantum mechanics. They investigated structural properties these posets. In paper, we study logical algebraic particular, investigate conditions under which they can be converted into operator residuated structures. ...

An (n,N)–connector of depth d is an acyclic digraph with n inputs and N outputs in which for any injective mapping of input vertices into output vertices there exist n vertex disjoint paths of length at most d joining each input to its corresponding output. In this paper we consider the problem of construction of sparse depth two connectors with n ≪ N . We use posets of star products and their ...

N-free posets have recently taken some importance and motivated many studies. This class of posets introduced by Grillet [8] and Heuchenne [11] are very related to another important class of posets, namely the series-parallel posets, introduced by Lawler [12] and studied by Valdes et al. [21]. This paper shows how N-free posets can be considered as generalizations of series-parallel posets, by ...

Given a partially ordered set P = (X,P), a function F which assigns to each x E X a set F(x) so that x ~<y in P if and only if F(x)C F(y) is called an inclusion representation. Every poser has such a representation, so it is natural to consider restrictions on the nature of the images of the function F. In this paper, we consider inclusion representations assigning to each x E X a sphere in ~d,...