Cartesian Closed Subcategories of CON T ≪ ∗ $CONT_{\ll }^{{\kern 8pt}\ast }$

Abstract

Let CONT be the category of continuous domains and Scott continuous mappings that preserve the way-below relation on domains. Let ω-ALG be the full subcategory of CONT consisting of all countably based algebraic domains, and FIN be the category of finite posets and monotone mappings. The main result proved in this paper is that FIN is the largest Cartesian closed full subcategory of ω-ALG . On the other hand, it is shown that the algebraic L-domains form a Cartesian closed full subcategory of ALG .