标题： 经济理论中的连续性公设：解构与整合 显示英文标题

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

摘要： 本文提出了六个定理和十个命题，可以看作是在Eilenberg、Wold、von Neumann-Morgenstern、Herstein-Milnor和Debreu的开创性工作的框架下，对连续性公设进行解构和整合。 其出发点是这样一个事实：应用于函数或二元关系的形容词“连续”并没有承认它所命名的概念可以赋予的多种含义，并且在各种技术数学结构下，这些含义可以被简化为新颖且意想不到的等价关系，这些关系在选择理论中被忽视了。 具体而言，它系统地研究了函数和二元关系的受限连续性和完全连续性之间的双向关系，在凸性、单调性和可微结构下，揭示了该公设的行为含义。 显示英文摘要

摘要： 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.