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Closure space has proven to be a useful tool to restructure lattices andvarious order structures.This paper aims to provide a novel approach tocharacterizing some important kinds of continuous domains by means of closurespaces. By introducing an additional map into a given closure space, the notionof F-augmented generalized closure space is presented. It is shown thatF-augmented generalized closure spaces generate exactly continuous domains.Moreover, the notion of approximable mapping is identified to representScott-continuous functions between continuous domains. These results produce acategory equivalent to that of continuous domains with Scottcontinuousfunctions. At the same time, two subclasses of F-augmented generalized closurespaces are considered which are representations of continuous L-domains andcontinuous bounded complete domains, respectively.

Categorical Representations of Continuous Domains and Continuous L-Domains Based on Closure Spaces