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Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions

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  • Bosi, Gianni
  • Caterino, Alessandro
  • Ceppitelli, Rita

Abstract

We present new sufficient conditions for the existence of a continuous utility function for an arbitrary binary relation on a topological space. Such conditions are basically obtained by using both the concept of a weakly continuous binary relation on a topological space and the concept of a countable network weight. In particular, we are concerned with suitable topological notions which generalize the concept of compactness and do not imply second countability or local compactness.

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File URL: http://mpra.ub.uni-muenchen.de/14808/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 14808.

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Date of creation: 04 Mar 2009
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Handle: RePEc:pra:mprapa:14808

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Keywords: hereditarily Lindeloef space; weakly continuous binary relation; countable network weight; hemicompactness; submetrizability;

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  1. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
  2. Back, Kerry, 1986. "Concepts of similarity for utility functions," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 129-142, April.
  3. Chateauneuf, Alain, 1987. "Continuous representation of a preference relation on a connected topological space," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 139-146, April.
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