Cartesian Closed Extensions of Subcategories of CONT

Abstract

In this paper we give a uniform way of proving cartesian closedness for many new subcategories of continuous posets. We define C-P to be the category of continuous posets whose D–completions are isomorphic to objects from C, where C is a subcategory of the category CONT of domains. The main result is that if C is a cartesian closed full subcategory of ALG⊥ or BC, then C-P is also a cartesian closed subcategory of the category CONTP of continuous posets and Scott continuous functions. In particular, we have the following cartesian closed categories : BC-P, LAT-P, aL-P, aBC-P, B-P, aLAT-P, ω-B-P, ω-aLAT-P, etc.