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

Bosi, Gianni and Caterino, Alessandro and Ceppitelli, Rita (2009): Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions.

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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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