发帖
雷达卡
摘要翻译：
本文全面地讨论了一个问题，即在一个连续性假设（即原则上不可检验的）存在下，二元关系是否可以是一致的（传递的）而不是决定性的（完全的），或者是决定性的而不是一致的，或者同时是不一致的或不决定性的。它确定了（选择）集的拓扑连通性，在这个选择集上，连续二元关系被定义为对这个问题至关重要。参照Eilenberg-Sonnenschein(ES)研究计划中的双向关系，给出了连通性的四个综合的、完整的刻画及其自然扩展；以及仅源于此的两个后果。这六个定理对经济和数学文献来说都是新颖的：它们推广了Eilenberg(1941)、Sonnenschein(1965)、Schmeidler(1971)和Sen(1969)的开创性结果，并与几个应用背景以及正在进行的理论工作有关。
---
英文标题：
《Topological Connectedness and Behavioral Assumptions on Preferences: A
Two-Way Relationship》
---
作者：
M. Ali Khan and Metin Uyan{\i}k
---
最新提交年份：
2018
---
分类信息：
一级分类：Economics 经济学
二级分类：Theoretical Economics 理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
--
一级分类：Mathematics 数学
二级分类：General Topology 一般拓扑
分类描述：Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties
连续统理论，点集拓扑，代数结构空间，基础，维数理论，局部和全局性质
--
---
英文摘要：
This paper offers a comprehensive treatment of the question as to whether a binary relation can be consistent (transitive) without being decisive (complete), or decisive without being consistent, or simultaneously inconsistent or indecisive, in the presence of a continuity hypothesis that is, in principle, non-testable. It identifies topological connectedness of the (choice) set over which the continuous binary relation is defined as being crucial to this question. Referring to the two-way relationship as the Eilenberg-Sonnenschein (ES) research program, it presents four synthetic, and complete, characterizations of connectedness, and its natural extensions; and two consequences that only stem from it. The six theorems are novel to both the economic and the mathematical literature: they generalize pioneering results of Eilenberg (1941), Sonnenschein (1965), Schmeidler (1971) and Sen (1969), and are relevant to several applied contexts, as well as to ongoing theoretical work.
---
PDF链接：
https://arxiv.org/pdf/1810.02004
京公网安备 11010802022788号
