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.
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Guo, L., Li, Q. The Categorical Equivalence Between Algebraic Domains and F-Augmented Closure Spaces. Order 32, 101–116 (2015). https://doi.org/10.1007/s11083-014-9318-8
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DOI: https://doi.org/10.1007/s11083-014-9318-8