Partial metrizability in value quantales

• Kopperman, Ralph D. ^[1] ; Matthews, S. ^[2] ; Pajoohesh, H. ^[3]
  1. [1] City University of New York

     City University of New York

     Estados Unidos

     
  2. [2] University of Warwick

     University of Warwick

     Reino Unido

     
  3. [3] University of Birmingham

     University of Birmingham

     Reino Unido

     

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 5, Nº. 1, 2004, págs. 115-127
• Idioma: inglés
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• Resumen

  • Partial metrics are metrics except that the distance from a point to itself need not be 0. These are useful in modelling partially defined information, which often appears in computer science. We generalize this notion to study “partial metrics” whose values lie in a value quantale which may be other than the reals. Then each topology arises from such a generalized metric, and for each continuous poset, there is such a generalized metric whose topology is the Scott topology, and whose dual topology is the lower topology. These are both corollaries to our result that a bitopological space is pairwise completely regular if and only if there is such a generalized metric whose topology is the first topology, and whose dual topology is the second.