Topologies Defined by Binary Relations
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.
|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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- Knoblauch, Vicki, 2005.
"Continuous lexicographic preferences,"
Journal of Mathematical Economics,
Elsevier, vol. 41(7), pages 812-825, November.
- Sprumont, Yves, 2001. "Paretian Quasi-orders: The Regular Two-Agent Case," Journal of Economic Theory, Elsevier, vol. 101(2), pages 437-456, December.
- Vicki Knoblauch, 2006. "Continuously Representable Paretian Quasi-Orders," Theory and Decision, Springer, vol. 60(1), pages 1-16, 02.
- 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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