Non-existence of continuous choice functions

Hiroki Nishimura and Efe Ok

Journal of Economic Theory, 2014, vol. 153, issue C, 376-391

Abstract: Let X be a compact, or path-connected, metric space whose topological dimension is at least 2. We show that there does not exist a continuous choice function (i.e., single-valued choice correspondence) defined on the collection of all finite feasible sets in X. Not to be void of content, therefore, a revealed preference theory in the context of most infinite consumption spaces must either relinquish the fundamental continuity property or allow for multi-valued choice correspondences.

Keywords: Choice functions; Rationality; Continuity (search for similar items in EconPapers)
JEL-codes: D11 D81 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:153:y:2014:i:c:p:376-391

DOI: 10.1016/j.jet.2014.07.006

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