Maximal classes of spaces and domains determined by topologies on function spaces of domains

In this paper, inspired by the work of Lawson and Xu, we consider the question of what classes A of topological spaces should be paired with classes B of domains in order that the Isbell and Scott topologies on function spaces [A→B] are identical for A∈A and B∈B. It is shown that: (1) if A and B are restricted to be a class of core compact spaces and a class of bicomplete domains respectively, a class of core compact and compact spaces is paired with a class of conditionally bounded complete domains; (2) if A and B are restricted to be a class of core compact and locally connected spaces and a class of bicomplete domains respectively, a class of topological spaces called RW-spaces (with finitely many connected components), which was first introduced by Kou and Luo and further studied by Lawson and Xu later, is paired with a class of pointed L-domains (disjoint union of pointed L-domains). This also gives a solution to a problem posed by Kou and Luo.