On the Largest Cartesian Closed Category of Stable Domains

Let SABC (resp., ) be the category of algebraic bounded complete domains with conditionally multiplicative mappings, that is, Scott-continuous mappings preserving meets of pairs of compatible elements (resp., stable mappings). Zhang showed that the category of dI-domains is the largest cartesian closed subcategory of ω-SABC and , with the exponential being the stable function space, where ω-SABC and are full subcategories of SABC and respectively which contain countablly based algebraic bounded complete domains as objects. This paper shows that:i)The exponentials of any full subcategory of SABC or are exactly function spaces;ii) the category of distributive algebraic bounded complete domains, is the largest cartesian closed subcategory of ; The compact elements of function spaces in the category SABC are also studied.