2021/08/26 by Metin Uyanik, M. Ali Khan, Uyanik, Metin +1
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #General Topology (math.GN) #Optimization and Control (math.OC) #Theoretical Economics (econ.TH) #econ.TH #math.GN #math.OC
paper · pdf · doi:10.48550/arxiv.2108.11736
arxiv created 2022/01/27 · arxiv updated 2022/01/28
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.