Rendiconti del Circolo Matematico di Palermo

, Volume 51, Issue 1, pp 151–162 | Cite as

Bicompleting weightable quasi-metric spaces and partial metric spaces

  • S. Oltra
  • S. Romaguera
  • E. A. Sánchez-Pérez
Article

Abstract

We show that the bicompletion of a weightable quasi-metric space is a weightable quasi-metric space. From this result we deduce that any partial metric space has an (up to isometry) unique partial metric bicompletion. Some other consequences are derived. In particular, applications to two interesting examples of partial metric spaces which appear in Computer Science, as the domain of words and the complexity space, are given.

AMS (2000) Subject classification

54-04 54E50 54C30 68Q25 68Q55 

Keywords

weightable quasi-metric partial metric bicompletion domain of words complexity space 

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References

  1. [1]
    Di Concilio A.,Spazi quasimetrici e topologie ad essi associate, Rend. Accad. Sci. Fis. Mat. Napoli,38 (1971), 113–130.MathSciNetGoogle Scholar
  2. [2]
    Escardo M. H.,PCF extended with real numbers, Theoretical Computer Science,162 (1996), 79–115.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Fletcher P., Lindgren W. F.,Quasi-uniform Spaces, Marcel Dekker, New York, (1982).MATHGoogle Scholar
  4. [4]
    Kahn G.,The semantics of a simple language for parallel processing, in: Proc. IFIP Congress, Elsevier North-Holland, Amsterdam,74 (1974), 471–475.Google Scholar
  5. [5]
    Künzi H. P. A.,Nonsymmetric topology, in: Proc. Szekszárd Conference, Bolyai Soc. Math. Studies,4 (1993), Hungary (Budapest 1995), 303–338.Google Scholar
  6. [6]
    Künzi H. P. A., Vajner V.,Weighted quasi-metric, in: Proc. 8th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci.,728 (1994), 64–77.CrossRefGoogle Scholar
  7. [7]
    Matthews S. G.,Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci.,728 (1994), 183–197.CrossRefMathSciNetGoogle Scholar
  8. [8]
    O’Neill S. J.,Partial metrics, valuations and domain theory, in: Proc. 11th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci.,806 (1996), 304–315.CrossRefMathSciNetGoogle Scholar
  9. [9]
    Romaguera S., Schellekens M.,Quasi-metric properties of complexity spaces, Topology Appl.,98 (1999), 311–322.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Salbany S.,Bitopological Spaces, Compactifications and Completions, Math. Monographs, Dept. Math. Univ. Cape Town,1 (1974).Google Scholar
  11. [11]
    Schellekens M.,The Smyth completion: a common foudation for denonational semantics and complexity analysis, in: Proc. MFPS 11, Electronic Notes in Theoretical Computer Science1 (1995), 211–232.CrossRefMathSciNetGoogle Scholar
  12. [12]
    Schellekens M.,On upper weightable spaces, in: Proc. 11th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci.,806 (1996), 348–363.CrossRefMathSciNetGoogle Scholar
  13. [13]
    Smyth M. B.,Totally bounded spaces and compact ordered spaces as domains of computation, in G. M. Reed, A. W. Roscoe and R. F. Wachter editors, Topology and Category Theory in Computer Science, Oxford University Press, (1991), 207–229.Google Scholar

Copyright information

© Springer 2002

Authors and Affiliations

  • S. Oltra
    • 1
  • S. Romaguera
    • 1
  • E. A. Sánchez-Pérez
    • 1
  1. 1.Escuela de Caminos Departamento de Matemática AplicadaUniversidad Politécnica de ValenciaValenciaSpain

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