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Continuous Utility Functions Through Scales

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Abstract

We present here a direct elementary construction of continuous utility functions on perfectly separable totally preordered sets that does not make use of the well-known Debreu’s open gap lemma. This new construction leans on the concept of a separating countable decreasing scale. Starting from a perfectly separable totally ordered structure, we give an explicit construction of a separating countable decreasing scale, from which we show how to get a continuous utility map.

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Correspondence to E. Induráin or C. Rodríguez-Palmero.

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Alcantud, J.C.R., Bosi, G., Campión, M.J. et al. Continuous Utility Functions Through Scales. Theory Decis 64, 479–494 (2008). https://doi.org/10.1007/s11238-007-9025-7

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  • DOI: https://doi.org/10.1007/s11238-007-9025-7

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