Applications of utility functions defined on quasi-metric spaces

A quasi-metric space (X, d) is called sup-separable if (X, ds ) is a separable metric space, where ds(x, y) = max{d(x, y), d(y, x)} for all x, y ∈ X. We characterize those preferences, defined on a sup-separable quasi-metric space, for which there is a semi-Lipschitz utility function. We deduce from our results that several interesting examples of quasi-metric spaces which appear in different fields of theoretical computer science admit semi-Lipschitz utility functions. We also apply our methods to the study of certain kinds of dynamical systems defined on quasi-metric spaces.  2003 Elsevier Inc. All rights reserved