A Representation of Lawson compact L-domains by information systems

In this paper, we investigate the information system representation of domain structures with certain topological property, to be specific, the information system representation of Lawson compact L-domains. Based on the characterization of Lawson compactness, we propose the notion of LCL-information systems and prove that LCL-information systems and Lawson compact L-domains can represent each other. Moreover, the notion of approximable mappings between LCL-information systems are introduced, which corresponds to Scott-continuous functions between Lawson compact L-domains. The equivalence of the category LCL-information systems with the category of Lawson compact L-domains is obtained. As a byproduct, we obtain a new information system representation for L-domains.