The continuity postulate in economic theory: A deconstruction and an integration

Metin Uyanık and M. Khan

Journal of Mathematical Economics, 2022, vol. 101, issue C

Abstract: This paper presents seven theorems and nine propositions that can be read as deconstructing and integrating the continuity postulate under the rubric of pioneering work of Eilenberg, Wold, von Neumann–Morgenstern, Herstein–Milnor and Debreu. Its point of departure is the fact that the adjective continuous applied to a function or a binary relation does not acknowledge the many meanings that can be given to the concept it names, and that under a variety of technical mathematical structures, its many meanings can be whittled down to novel and unexpected equivalences that have been missed in the theory of choice. Specifically, it provides a systematic investigation of the two-way relation between restricted and full continuity of a function and a binary relation that, under convex, monotonic and differentiable structures, draws out the behavioral implications of the postulate.

Keywords: Archimedean; Arc-continuous; Wold-continuous; Linear-continuous; Section-continuous; Mixture-continuous (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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Working Paper: The Continuity Postulate in Economic Theory: A Deconstruction and an Integration (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:101:y:2022:i:c:s0304406822000507

DOI: 10.1016/j.jmateco.2022.102704

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