Direct Approaches for Representations of Various Algebraic Domains via Closure Spaces

In this paper, F-augmented closure spaces are generalized to F-closure spaces, and the concept of F-closed sets are introduced. Properties of their ordered structures are investigated. Representations of various algebraic domains such as algebraic lattices, algebraic L-domains, BF-domains via F-closure spaces are considered. As applications of these methods, more direct approaches to representing various algebraic domains via classical closure space are given, respectively. F-relations between F-closure spaces are defined and properties of them are examined. It is also proved that the category of algebraic domains with Scott continuous maps is equivalent to that of F-closure spaces with F-relations.