Mfcsit 2002

A thorough understanding of function spaces is useful for identifying large cartesian closed categories of topological spaces and domains. We consider the question of what classes A of spaces should be paired with classes B of domains so that all function spaces [A B] are #-compact domains. We observe that in general the class B forms what we call a domain variety, a class of domains closed under products, continuous retracts, and Scott-closed subsets. Specific sample solutions are that core compact spaces are paired with bounded complete domains and a special class of locally connected core compact spaces called RW-spaces is paired with the class of #-compact pointed L-domains