Applications of utility functions defined on quasi-metric spaces
By generalizing some known results from metric to quasi-pseudometric \(T_0\)-spaces the authors show that certain methods developed in mathematical economics can be successfully applied to problems in theoretical computer science. In the first part of their article they characterize those preferences, defined on a sup-separable quasi-pseudometric \(T_0\)-space, for which there is a semi-Lipschitz utility function. They deduce that several interesting examples of quasi-pseudometric spaces which appear in domain theory and complexity theory admit semi-Lipschitz utility functions. In the second part of their article they apply their methods to a study of certain dynamical systems defined on quasi-pseudometric \(T_0\)-spaces. The examples discussed in the first part are used to illustrate various results, for instance some statements on attractors.
scientific article; zbMATH DE number 1970521
scientific article