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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
  • R-Separable System
  • R-Normal Space
  • Continuous Utility Function
  • Equivalence Theorem
Disciplines
  • Mathematics

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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