The Categorical Equivalence Between Domains and Interpolative Generalized Closure Spaces

Studia Logica 111 (2):187-215 (2023)
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Closure space has been proven to be a useful tool to restructure lattices and various order structures. This paper aims to provide an approach to characterizing domains by means of closure spaces. The notion of an interpolative generalized closure space is presented and shown to generate exactly domains, and the notion of an approximable mapping between interpolative generalized closure spaces is identified to represent Scott continuous functions between domains. These produce a category equivalent to that of domains with Scott continuous functions. Meanwhile, some important subclasses of domains are discussed, such as algebraic domains, _L_-domains, bounded-complete domains, and continuous lattices. Conditions are presented which, when fulfilled by an interpolative generalized closure space, make the generated domain fulfill some restrictive conditions.



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Domain theory in logical form.Samson Abramsky - 1991 - Annals of Pure and Applied Logic 51 (1-2):1-77.
Continuous L-domains in logical form.Longchun Wang, Qingguo Li & Xiangnan Zhou - 2021 - Annals of Pure and Applied Logic 172 (9):102993.

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