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Continuous Utility Functions Through Scales |
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| Authors: | J. C. R. Alcantud G. Bosi M. J. Campión J. C. Candeal E. Induráin C. Rodríguez-Palmero |
| Affiliation: | (1) Facultad de Economía y Empresa, Universidad de Salamanca, E-37008 Salamanca, Spain;(2) Dipartimento di Matematica Applicata “Bruno de Finetti”, Università di Trieste, Piazzale Europa 1, I-34127 Trieste, Italy;(3) Departamento de Matemáticas, Universidad Pública de Navarra, Campus Arrosadía, E-31006 Pamplona, Spain;(4) Facultad de Ciencias Económicas y Empresariales, Departamento de Análisis Económico, Universidad de Zaragoza, c/ Doctor Cerrada 1-3, E-50005 Zaragoza, Spain;(5) Facultad de Ciencias Económicas y Empresariales, Universidad de Valladolid, Av. Valle, Esgueva, 6, E-47011 Valladolid, Spain |
| 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. |
| Keywords: | total preorders continuous utility representations separating scales decreasing scales |
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