The Categorical Equivalence Between Algebraic Domains and F-Augmented Closure Spaces

Abstract

We introduce the notion of F-augmented closure spaces by incorporating an additional structure (a family of finite subsets of the underlying set) into a given closure space in an appropriate way. We also introduce the notion of F-morphisms between F-augmented closure spaces and establish the equivalence between the category of F-augmented closure spaces and that of algebraic domains with Scott continuous maps as morphisms. Our results provide a novel approach to representing algebraic domains by means of closure spaces.