The way-below relation of function spaces over semantic domains

The way-below relation of function spaces over semantic domains

For partially ordered sets that are continuous in the sense of D. S. Scott, the waybelow relation is crucial. It expresses the approximation of an ideal element by its finite parts. We present explicit characterizations of the way-below relation on spaces of continuous functions from topological spaces into continuous posets. Although it is well-known in which cases these function spaces are co...

The “ Way - Below ” Relation

In the paper the “way-below” relation, in symbols x y, is introduced. Some authors prefer the term “relatively compact” or “way inside”, since in the poset of open sets of a topology it is natural to read U V as “U is relatively compact in V ”. A compact element of a poset (or an element isolated from below) is defined to be way below itself. So, the compactness in the poset of open sets of a t...

A new class of function spaces on domains of R^d and its relations to classical function spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

a new class of function spaces on domains of r^d and its relations to classical function spaces