(Hemi)continuity of additive preference preorders |
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| Institution: | School of Economics & Finance, University of St Andrews, KY16 9AL, St Andrews, UK;LEMMA, Université Panthéon-Assas, Paris II, 4 rue Blaise Desgoffe, 75006 Paris, France;Department of Operations and Information Management, University of Connecticut, 2100 Hillside Road Unit 1041, Storrs, CT 06269-1041, USA;Université de Montréal et CIREQ, Canada;1-14-13 Ainokawa, Ichikawa, Chiba, 272-0143, Japan;Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada T6G 2G1;Department of Economics, Rutgers University, 75 Hamilton Street, New Brunswick, NJ 08901, USA |
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| Abstract: | It is shown that the two common notions of topological continuity for preference preorders, which require closed contour sets and a closed graph respectively, are equivalent even when completeness is not assumed, provided that the domain is a normed linear space or a topological group and the preorder is additive. |
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| Keywords: | Incompleteness Continuity Hemicontinuity Additivity Independence Homotheticity |
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