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


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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G. Gierz , K. H. Hofmann , K. Keimel , J. D. Lawson , M. Mislove and D. S. Scott (2003) Continuous Lattices and Domains, Encyclopedia of Mathematics and its Applications 93, Cambridge University Press.

H. P. A. Künzi (2001) Nonsymmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology. In: C.E. Aull and R. Lowen (eds.) Handbook of the History of General Topology 3, Kluwer853968.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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