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Topologies Defined by Binary Relations

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  • Vicki Knoblauch

    (University of Connecticut)

Abstract

The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies induced by binary relations and present topological versions of two classical preference representation theorems. We then use our characterizations to construct examples of topologies that are not induced by binary relations. We also present examples that illustrate our topological preference representation results. The preference literature contains characterizations of order topologies, that is, topologies induced by total preorders, but ours are the first characterizations of topologies induced by binary relations that are not neccesarily total preorders.

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File URL: http://www.econ.uconn.edu/working/2009-28r.pdf
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File URL: http://www.econ.uconn.edu/working/2009-28.pdf
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Bibliographic Info

Paper provided by University of Connecticut, Department of Economics in its series Working papers with number 2009-28.

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Length: 17 pages
Date of creation: Sep 2009
Date of revision: Dec 2009
Handle: RePEc:uct:uconnp:2009-28

Note: This paper previously circulated under the title "Order Topologies: Characterizations and Counterexamples." I would like to thank Esteban Indurain for many valuable suggestions.
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Postal: University of Connecticut 341 Mansfield Road, Unit 1063 Storrs, CT 06269-1063
Phone: (860) 486-4889
Fax: (860) 486-4463
Web page: http://www.econ.uconn.edu/
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Related research

Keywords: consumer preferences; order topology; preference representation;

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References

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  1. Vicki Knoblauch, 2006. "Continuously Representable Paretian Quasi-Orders," Theory and Decision, Springer, vol. 60(1), pages 1-16, 02.
  2. Vicki Knoblauch, 2003. "Continuous Lexicographic Preferences," Working papers 2003-31, University of Connecticut, Department of Economics.
  3. Sprumont, Yves, 2001. "Paretian Quasi-orders: The Regular Two-Agent Case," Journal of Economic Theory, Elsevier, vol. 101(2), pages 437-456, December.
  4. Chateauneuf, Alain, 1987. "Continuous representation of a preference relation on a connected topological space," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 139-146, April.
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