Summary
We characterize continuous representability of preference relations by multiplicative functions and by certain polynomial functions, on connected topological spaces. Our methods show that the same Continuity Principle that yielded additive utility representations in earlier work applies much more generally.
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Fuhrken, G., Richter, M.K. Polynomial utility. Econ Theory 1, 231–249 (1991). https://doi.org/10.1007/BF01210562
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DOI: https://doi.org/10.1007/BF01210562