•  105
    Continuous Utility Functions Through Scales
    with J. C. R. Alcantud, M. J. Campión, J. C. Candeal, E. Induráin, and C. Rodríguez-Palmero
    Theory and Decision 64 (4): 479-494. 2007.
    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