Skip to main content
SpringerLink
Log in

Maximal Classes of Topological Spaces and Domains Determined by Function Spaces

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

Abstract

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).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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.

  2. Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M. and Scott, D.: A Compendium of Continuous Lattices, Springer-Verlag, Berlin, 1980.

    Google Scholar 

  3. Gierz, G., Hofmann, K., Keimel, K., Lawson, J. D., Mislove, M. and Scott, D.: Continuous Lattices and Domains, Cambridge University Press, 2003.

  4. Jung, A.: Cartesian closed categories of domains, Ph.D. Thesis, Technische Hochschule Darmstadt, 1988.

    Google Scholar 

  5. Kou, H. and Luo, M.: RW-spaces and compactness of function spaces for L-domains, to appear.

  6. Lawson, J. D. and Xu, L.: When does the class [A → B] consist of continuous domains? Topology and its Applications 130 (2003), 91–97.

    Google Scholar 

  7. 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.

  8. Liang, J. and Keimel, K.: Compact continuous L-domains, Computers & Mathematics with Applications 38 (1999), 81–89.

    Google Scholar 

  9. Xu, L.: External characterizations of continuous sL-domains, to appear.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA

    Jimmie D. Lawson

  2. Department of Mathematics, Yangzhou University, Yangzhou, 225002, P. R. China

    Luoshan Xu

Authors
  1. Jimmie D. Lawson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luoshan Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lawson, J.D., Xu, L. Maximal Classes of Topological Spaces and Domains Determined by Function Spaces. Applied Categorical Structures 11, 391–402 (2003). https://doi.org/10.1023/A:1024493004302

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024493004302

Search

Navigation