Abstract. In this paper we establish some properties of fuzzy quasi-pseudo-metric spaces. An important result is that any partial ordering can be defined by a fuzzy quasi-metric, which can be applied both in theoretical computer science and in information theory, where it is usual to work with sequences of objects of increasing information. We also obtain decomposition theorems of a fuzzy quasi...

(2) Let L, S, T be complete non empty posets, f be a CLHomomorphism of L, S, and g be a CLHomomorphism of S, T . Then g · f is a CLHomomorphism of L, T . (3) For every non empty relational structure L holds idL is infs-preserving. (4) For every non empty relational structure L holds idL is directed-sups-preserving. (5) For every complete non empty poset L holds idL is a CLHomomorphism of L, L. ...

Let D denote the partially ordered sets of homomorphism classes of finite directed graphs, ordered by the homomorphism relation. Order theoretic properties of this poset have been studied extensively, and have interesting connections to familiar graph properties and parameters. This paper studies the generalized duality pairs in D: it gives a new, short proof for the Foniok Nešetřil Tardif theo...

provide the notation and terminology for this paper. 1. POSET RETRACTS One can prove the following propositions: (1) For all binary relations a, b holds a · b = a b. (2) Let X be a set, L be a non empty relational structure, S be a non empty relational substruc-ture of L, f , g be functions from X into the carrier of S, and f , g be functions from X into the carrier of L. If f = f and g = g and...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

A non-empty subset of a topological space is irreducible if whenever it is covered by the union of two closed sets, then already it is covered by one of them. Irreducible sets occur in proliferation: (1) every singleton set is irreducible, (2) directed subsets (which of fundamental status in domain theory) of a poset are exactly its Alexandroff irreducible sets, (3) directed subsets (with respe...

Given a directed graph G = (V,E) and an integer k ≥ 1, a ktransitive-closure-spanner (k-TC-spanner) of G is a directed graph H = (V,EH) that has (1) the same transitive-closure as G and (2) diameter at most k. Transitive-closure spanners are a common abstraction for applications in access control, property testing and data structures. We show a connection between 2-TC-spanners and local monoton...

In this paper we introduce the notion of the fractional weak discrepancy of a poset, building on previous work on weak discrepancy in [5, 8, 9]. The fractional weak discrepancy wdF (P ) of a poset P = (V,≺) is the minimum nonnegative k for which there exists a function f : V → R satisfying (1) if a ≺ b then f(a) + 1 ≤ f(b) and (2) if a ‖ b then |f(a)− f(b)| ≤ k. We formulate the fractional weak...

Given a bipartite graph, let us pick an acyclic orientation of its edges. Then, if we consider the partially ordered set (poset) induced by this orientation, the number of linear extensions of such a poset is maximal whenever the orientation is bipartite, or such that no directed path of length two exists. We define a sequence of automorphisms that injectively but nonbijectively map the set of ...

1. Introduction. Let A" be a partially ordered set (poset) with respect to a relation ^, and possessing least and greatest elements O and / respectively. Let us call a subset S of A" up-directed (down-directed) if and only if for all xES and y ES there exists zGS such that 3^x, z^y (z^x, z^y). Following McShane [2], we call a subset K of X Dedekind-closed if and only if whenever S is an up-dire...