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    • 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.



    Titolo: Continuous utility functions through scales
    Autori: 
    BOSI, GIANNI
    mostra contributor esterni 
    Data di pubblicazione: 2008
    Rivista: 
    THEORY AND DECISION  
    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): 10.1007/s11238-007-9025-7
    Appare nelle tipologie:1.1 Articolo in Rivista

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