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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.

Suggested Citation

  • Vicki Knoblauch, 2009. "Topologies Defined by Binary Relations," Working papers 2009-28, University of Connecticut, Department of Economics, revised 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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    References listed on IDEAS

    as
    1. 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.
    2. Sprumont, Yves, 2001. "Paretian Quasi-orders: The Regular Two-Agent Case," Journal of Economic Theory, Elsevier, vol. 101(2), pages 437-456, December.
    3. Knoblauch, Vicki, 2005. "Continuous lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 812-825, November.
    4. Vicki Knoblauch, 2006. "Continuously Representable Paretian Quasi-Orders," Theory and Decision, Springer, vol. 60(1), pages 1-16, February.
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    More about this item

    Keywords

    consumer preferences; order topology; preference representation;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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