Pointwise Debreu Lexicographic Powers |
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Authors: | Alfio Giarlotta Stephen Watson |
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Institution: | 1.Department of Economics and Quantitative Methods,University of Catania,Catania,Italy;2.Department of Mathematics and Statistics,York University,Toronto,Canada |
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Abstract: | A linear ordering is Debreu (respectively, pointwise Debreu) if each of its suborderings can be mapped into it with an order-preserving
function that is both injective (respectively, locally injective) and continuous (respectively, locally continuous) with respect
to the order topology on both spaces. Each Debreu linear ordering is pointwise Debreu, but the converse does not hold. In
the context of utility representations in mathematical economics, it has been proved that any lexicographic power with an
uncountable exponent fails to be Debreu. We sharpen this result by analyzing lexicographic powers that are pointwise Debreu. |
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