# On some equivalent approaches to Mathematical Utility Theory

- Authors
- Journal
- Mathematical Social Sciences 0165-4896
- Publisher
- Elsevier
- Publication Date
- Volume
- 29
- Issue
- 1
- Identifiers
- DOI: 10.1016/0165-4896(94)00761-v
- Keywords
- Disciplines

## Abstract

Abstract In this paper a fundamental result is proved which shows, in particular, that the continuous representation theorems of Eilenberg, Debreu, Peleg, Herden, the Debreu Open Gap Theorem, the Beardon Weak Open Gap Theorem, Nachbin's Separation Theorem, the Cantor Characterization Theorem of the linear continuum and, in addition, Urysohn's Separation Theorem and the Alexandroff-Urysohn Metrization Theorem can be considered to be equivalent to one another. This result, therefore, finishes a development initiated by Mehta which combines the basic approaches to mathematical utility theory with some of the most important results of elementary topology.

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