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.
Continuous utility functions through scales / Alcantud, J. C. R.; Bosi, Gianni; Campion, M. J.; Candeal, J. C.; Indurain, E; RODRIGUEZ PALMERO, C.. - In: THEORY AND DECISION. - ISSN 0040-5833. - STAMPA. - 64:(2008), pp. 479-494. [10.1007/s11238-007-9025-7]
Continuous utility functions through scales
BOSI, GIANNI;
2008-01-01
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.Pubblicazioni consigliate
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