A Characterization Theorem for Continuous Lattices by Closure Spaces
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.
KeywordsClosure space Approximable mapping Continuous lattice
- 3.Erné, M.: Lattice representations for categories of closure spaces, Categorical topology (Toledo, OH, 1983). Bentley, H.L. (ed.) Sigma Series in Pure Mathematics, vol. 5, pp. 197–222. Heldermann, Berlin (1984)Google Scholar
- 10.Hofmann, K.H., Keimel, K.: A General Character Theory for Partially Osets and Lattices, vol. 122, no. 122. Memoirs of the American Mathematical Society (1972)Google Scholar