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Published in:
2010 | OriginalPaper | Chapter
Continuous Utility Functions for Nontotal Preorders: A Review of Recent Results
Authors : Gianni Bosi, Romano Isler
Published in: Preferences and Decisions
Publisher: Springer Berlin Heidelberg
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We present some recent and significant results concerning the existence of a continuous utility function for a not necessarily total preorder on a topological space.We first recall an appropriate continuity concept (namely,
weak continuity
) relative to a preorder on a topological space. Then a general characterization of the existence of a continuous utility function for a not necessarily total preorder on a topological space is presented and some consequences of this basic result are produced.