Partial metrizability in value quantales

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