In this paper we study an astonishing similarity between the utility representation problem in economics and the entropy representation problem in thermodynamics.

In this note we consider some problems involved in proving the existence of a continuous real-valued utility function representing a preference relation. We claim that there is an error in the classical Rader proof of the existence of an upper semicontinuous utility function. We also pose some...

It is shown that each of the Debreu Open Gap Theorem and the Debreu Continuous Utility Representation Theorem can be used in order to prove the other. Furthermore, it is proved that the classical Alexandroff-Urysohn Metrization Theorem implies Debreu's Continuous Utility Representation Theorem...