Skip to main content
SpringerLink
Log in

Quasi-uniformities: Reconciling domains with metric spaces

  • Part III Domain Theory
  • Conference paper
  • First Online:
Mathematical Foundations of Programming Language Semantics (MFPS 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 298))

Abstract

We show that quasi-metric or quasi-uniform spaces provide, inter alia, a common generalization of cpo's and metric spaces as used in denotational semantics. To accommodate the examples suggested by computer science, a reworking of basic notions involving limits and completeness is found to be necessary. Specific results include general fixed point theorem and a sequential completion construction.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Berthiaume, On quasi-uniformities in hyperspaces, Proc. Am. Math. Soc. 66 (1977), 335–342.

    Google Scholar 

  2. N. Bourbaki, Elements of Mathematics. General Topology; Part 1 Addison-Wesley 1966.

    Google Scholar 

  3. A.Csaszar, Foundationsof General Topology, Pergamon 1963.

    Google Scholar 

  4. P.Fletcher, W.Lindgren, Quasi-uniform Spaces, Marcel Dekker 1982.

    Google Scholar 

  5. M. Hennessy, G. Plotkin, A term model for CCS, Proc. 9th MFCS, LNCS 88 (1980), 261–274.

    Google Scholar 

  6. G.Gierz et al., A Compendium of Continuous Lattices, Springer 1980.

    Google Scholar 

  7. F. Lawvere, Metric spaces, generalized logic, and closed categories Rend. del Sem. Mat. e Fis. di Milano XLIII (1973), 135–166.

    Google Scholar 

  8. N. Levine, W. Stager, On the hyperspace of a quasi-uniform space, Math. J. Okayama Univ. 15 (1971–2), 101–106.

    Google Scholar 

  9. A.Melton, D.Schmidt, A topological framework for cpo's lacking bottom elements, Unpublished memo (1985).

    Google Scholar 

  10. R. Milner, A modal characterization of observable machine behaviour CAAP '81, LNCS 112 (1981), 25–34.

    Google Scholar 

  11. R.Milner, A Calculus of Communicating Sequences, Springer LNCS 92 1980.

    Google Scholar 

  12. G.Plotkin, Lecture Notes on Domain Theory (Edinburgh: unpublished)

    Google Scholar 

  13. D. Scott, Domains for denotational semantics, ICALP '82, LNCS 140 (1982), 577–613.

    Google Scholar 

  14. M. Smyth, Power domains and predicate transformers, ICALP '83, LNCS 154 (1983), 662–675.

    Google Scholar 

  15. M. Smyth, Finite approximation of spaces, Category Theory and Computer Programming, ed. D.Pitt et al., LNCS 240 (1986), 225–241.

    Google Scholar 

  16. M.Smyth, Quasi-uniformities as a unifying theme, Unpublished ms., 1986.

    Google Scholar 

  17. M. Hennessy, R. Milner, On observing nondeterminism and concurrency ICALP '80, LNCS 85 (1980), 299–309.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computing, Imperial College, SW7, London

    M. B. Smyth

Authors
  1. M. B. Smyth
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

M. Main A. Melton M. Mislove D. Schmidt

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Smyth, M.B. (1988). Quasi-uniformities: Reconciling domains with metric spaces. In: Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Language Semantics. MFPS 1987. Lecture Notes in Computer Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19020-1_12

Download citation

  • DOI: https://doi.org/10.1007/3-540-19020-1_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19020-2

  • Online ISBN: 978-3-540-38920-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation