Jointly continuous utility functions on submetrizable k(omega)-spaces

摘要

A Hausdorff topological space X is a submetrizable k(omega)-space if it is the inductive limit of an increasing sequence of metric compact subspaces of X. These spaces have nice properties and they seem to be very interesting in the study of the utility representation problem. Every closed preorder on a submetrizable k(omega)-space has a continuous utility representation and some theorems on the existence of jointly continuous utility functions have been recently proved.