Open gaps, metrization and utility

Gerhard Herden and Ghanshyam B. Mehta
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Gerhard Herden: Department of Mathematics and Computer Science, University of Essen, D-45117 Essen, GERMANY
Ghanshyam B. Mehta: Department of Economics, University of Queensland, St. Lucia, Qld. 4067, AUSTRALIA

Economic Theory, 1996, vol. 7, issue 3, 546 pages

Abstract: 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 and, thus, all known results on the existence of continuous utility functions.

Date: 1996
Note: Received: August 24, 1993; revised version March 28, 1994
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