Topologies Defined by Binary Relations
AbstractThe 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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Bibliographic InfoPaper provided by University of Connecticut, Department of Economics in its series Working papers with number 2009-28.
Length: 17 pages
Date of creation: Sep 2009
Date of revision: Dec 2009
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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More information through EDIRC
consumer preferences; order topology; preference representation;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-09-26 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Knoblauch, Vicki, 2005.
"Continuous lexicographic preferences,"
Journal of Mathematical Economics,
Elsevier, vol. 41(7), pages 812-825, November.
- Vicki Knoblauch, 2006. "Continuously Representable Paretian Quasi-Orders," Theory and Decision, Springer, vol. 60(1), pages 1-16, 02.
- Sprumont, Yves, 2001. "Paretian Quasi-orders: The Regular Two-Agent Case," Journal of Economic Theory, Elsevier, vol. 101(2), pages 437-456, December.
- 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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