Open gaps, metrization and utility

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.

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Year of publication:	1996
Authors:	Herden, Gerhard ; Mehta, Ghanshyam B.
Published in:	Economic Theory. - Springer. - Vol. 7.1996, 3, p. 541-546
Publisher:	Springer

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Type of publication:	Article
Notes:	Received: August 24, 1993; revised version March 28, 1994
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005753119