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  • Mathematical Structures in Computer Science, Volume 20, Issue 3
  • June 2010, pp. 453-472

Domain theoretic characterisations of quasi-metric completeness in terms of formal balls

  • SALVADOR ROMAGUERA (a1) and OSCAR VALERO (a2)
  • DOI: http://dx.doi.org/10.1017/S0960129510000010
  • Published online: 07 April 2010
Abstract

We characterise those quasi-metric spaces (X, d) whose poset BX of formal balls satisfies the condition (*) From this characterisation, we then deduce that a quasi-metric space (X, d) is Smyth-complete if and only if BX is a dcpo satisfying condition (*). We also give characterisations in terms of formal balls for sequentially Yoneda complete quasi-metric spaces and for Yoneda complete T1 quasi-metric spaces. Finally, we discuss several properties of the Heckmann quasi-metric on the formal balls of any quasi-metric space.

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  • ISSN: 0960-1295
  • EISSN: 1469-8072
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