Partial metrizability in value quantales

[EN] 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.This author wishes to acknowledge support for this research from the EPSRC of the United Kingdom (grant GR/S07117/01), and from the City University of New York (PSCCUNY grant 64472-00 33).Kopperman, RD.; Matthews, S.; Pajoohesh, H. (2004). Partial metrizability in value quantales. Applied General Topology. 5(1):115-127. doi:10.4995/agt.2004.2000.SWORD1151275