A characterization theorem for continuous lattices by closure spaces

Abstract

The notion of closure spaces plays an important role in formal concept analysis, and there exists a close connection between formal concept analysis and lattice theory. In order to restructure continuous lattices, a special kind of complete lattices in Domain theory, this paper proposes a novel notion named relationally consistent F-augmented closure spaces. Then, the concept of F-approximable mappings between relationally consistent F-augmented closure spaces is introduced, which provides a representation of Scott continuous maps between continuous lattices. The final result is: the categories of relationally consistent F-augmented closure spaces and continuous lattices are equivalent.