Maximal Classes of Topological Spaces and Domains Determined by Function Spaces

In this paper the question of what classes A of T0-spaces should be paired with classes ℬ of domains in order that all function spaces [A→B] for A∈A and B∈ℬ are λ-compact domains is considered. It is shown that core compact spaces are paired with bounded complete domains and a class of topological spaces called RW-spaces (with finitely many components) is paired with the class of λ-compact pointed L-domains (L-domains).