Maximal Classes of Topological Spaces and Domains Determined by Function Spaces

Applied Categorical Structures - Tập 11 - Trang 391-402 - 2003
Jimmie D. Lawson1, Luoshan Xu2
1Department of Mathematics, Louisiana State University, Baton Rouge, USA
2Department of Mathematics, Yangzhou University, Yangzhou, P. R. China

Tóm tắt

In this paper the question of what classes A of T 0-spaces should be paired with classes ℬ of domains in order that all function spaces [A→B] for A∈A and B∈ℬ are λ-compact domains is considered. It is shown that core compact spaces are paired with bounded complete domains and a class of topological spaces called RW-spaces (with finitely many components) is paired with the class of λ-compact pointed L-domains (L-domains).

Tài liệu tham khảo

Abramsky, S. and Jung, A.: Domain theory, in S. Aramsky, D.M. Gabbay and T. S. E. Maibaum (eds), Handbook of Logic in Computer Science, Vol. 3, Clarendon Press, 1994, pp. 1–168. Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M. and Scott, D.: A Compendium of Continuous Lattices, Springer-Verlag, Berlin, 1980. Gierz, G., Hofmann, K., Keimel, K., Lawson, J. D., Mislove, M. and Scott, D.: Continuous Lattices and Domains, Cambridge University Press, 2003. Jung, A.: Cartesian closed categories of domains, Ph.D. Thesis, Technische Hochschule Darmstadt, 1988. Kou, H. and Luo, M.: RW-spaces and compactness of function spaces for L-domains, to appear. Lawson, J. D. and Xu, L.: When does the class [A → B] consist of continuous domains? Topology and its Applications 130 (2003), 91–97. Lawson, J. D. and Mislove, M.: Problems in domain theory and topology, in J. Van Mill and G. M. Reed (eds), Open Problems in Topology, Elsevier, 1990, pp. 351–372. Liang, J. and Keimel, K.: Compact continuous L-domains, Computers & Mathematics with Applications 38 (1999), 81–89. Xu, L.: External characterizations of continuous sL-domains, to appear.