nets, useful topological tools, used to generalize certainconcepts that may only be general enough in the context of metricspaces. in this work we introduce this concept in an $s$-poset, aposet with an action of a posemigroup $s$ on it whichis a very useful structure in computer sciences and interestingfor mathematicians, and give the the concept of $s$-net. using $s$-nets and itsconvergency we...

Call a topology well if and only if every open is compact. The starting point of this note is that this notion generalizes that of well-quasi order, in the sense that an Alexandroff topology is well if and only if its specialisation quasi-ordering is well. For more general topologies, this opens the way to verifying infinite transition systems based on non-well quasi ordered sets, but where the...

We study a generalized notion of topology which evolved from applications in the area of logic programming semantics The generalization is obtained by relaxing the requirement that a neighbourhood of a point includes the point itself and by allowing neighbourhoods of points to be empty We show that it is meaningful to discuss neighbourhoods convergence and continuity in these spaces A generaliz...