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The Continuity Postulate in Economic Theory: A Deconstruction and an Integration

Metin Uyanik and M. Khan ()

Papers from arXiv.org

Abstract: This paper presents six theorems and ten 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.

Date: 2021-08, Revised 2022-01
New Economics Papers: this item is included in nep-hpe and nep-isf
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