Continuous valuations have been proposed by several authors as a way of modeling probabilistic non-determinism in programming language semantics. Let (X;O) be a topological space. A quasi-simple valuation on X is the sup of a directed family of simple valuations. We show that quasisimple valuations are exactly those valuations that extend to continuous valuations to the Alexandroff topology on ...

This article is concerned with Alexandroff L-topological spaces and L-co-topological spaces, where L is a commutative, unital quantale. On one hand, an example is given to show that there is a finite strong L-topological space that is not Alexandroff. On the other hand, it is proved that every finite strong L-co-topological space is Alexandroff and that the category of Alexandroff strong L-co-t...

let g = (v,e) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. in this paper, we associate a topology to g, called graphic topology of g and we show that it is an alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. then we investigate some properties of this topology. our motivation is to give an e...

Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...

Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersection of each family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an elem...

In this paper, we study the correspondence between graphs and Alexandroff spaces. It is shown that a topological space \(X\) if only graph equipped with \(X\)-right topology.

On one hand the graph isomorphism problem (GI) has received considerable attention due to its unresolved complexity status and its many practical applications. On the other hand a notion of compatible topologies on graphs has emerged from digital topology (see [5, 7, 17, 9, 14, 16]). In this article we study GI from the topological point of view. Firstly we explore the poset of compatible topol...

In this paper, we define and study a new topology constructed from any given topology on a set, using irreducible sets. The manner in which this derived topology is obtained is inspired by how the Scott topology on a poset is constructed from its Alexandroff topology. This derived topology leads us to a weak notion of sobriety called k-bounded sobriety. We investigate the properties of this der...

We show that if X is a locally compact, paracompact and Hausdorff space, then X can be realised as the subspace of all maximal points of the inverse limit of an inverse system of partial orders with an appropriate topology (equivalently T0-Alexandroff spaces). Then, the space X is homeomorphic to a deformation retract of that limit. Moreover, we extend results obtained by Clader and Thibault an...