Maximal Classes of Topological Spaces and Domains Determined by Function Spaces

In this paper the question of what classes A of T ₀-spaces should be paired with classes of domains in order that all function spaces AB] for AA and B are -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 -compact pointed L-domains (L-domains).