Partial metrizability in value quantales


  • Ralph D. Kopperman City University of New York
  • S. Matthews University of Warwick Coventry
  • H. Pajoohesh University of Birmingham



Value lattice, partial metric, Quasimetric, Completely regular bitopological space, Value quantale, Well above, Auxiliary relation


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.


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Author Biographies

Ralph D. Kopperman, City University of New York

Department of Mathematics

S. Matthews, University of Warwick Coventry

Department of Computer Science

H. Pajoohesh, University of Birmingham

Department of Mathematics Shahid Beheshti University Teheran, IRAN.

BCRI and CEOL, University College Cork, Ireland.

Department of Computer Science, University of Birmingham, UK.


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How to Cite

R. D. Kopperman, S. Matthews, and H. Pajoohesh, “Partial metrizability in value quantales”, Appl. Gen. Topol., vol. 5, no. 1, pp. 115–127, Apr. 2004.



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