ON SOME EQUIVALENT APPROACHES TO MATHEMATICAL UTILITY-THEORY

In this paper a fundamental result is proved which shows, in particula r, that the continuous representation theorems of Eilenberg, Debreu, P eleg, Herden, the Debreu Open Gap Theorem, the Beardon Weak Open Gap T heorem, Nachbin's Separation Theorem, the Cantor Characterization Theo rem of the linear continuum and, in addition, Urysohn's Separation The orem and the Alexandroff-Urysohn Metrization Theorem can be considered to be equivalent to one another. This result, therefore, finishes a d evelopment initiated by Mehta which combines the basic approaches to m athematical utility theory with some of the most important results of elementary topology.