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EnglishWe 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.
| Titolo: | Continuous utility functions through scales |
| Autori: | |
| Data di pubblicazione: | 2008 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11368/1709692 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s11238-007-9025-7 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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