Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions

Abstract

We present new sufficient conditions for the existence of a continuous
utility function for an arbitrary binary relation on a topological space.
Such conditions are basically obtained by using both the concept of a
weakly continuous binary relation on a topological space and the concept
of a network weight. We are concerning with suitable topological
notions which generalize the concept of compactness and do not imply
second countability or local compactness.