拓扑连通性与偏好行为假设的双向关系
Topological Connectedness and Behavioral Assumptions on Preferences: A Two-Way Relationship
摘要：
本文提供了一个全面的治疗的问题，是否二元关系可以是一致的（传递），而不是决定性的（完整的），或决定性的，而不是一致的，或同时不一致或不确定的，在存在的连续性假设，原则上，不可检验的。它确定拓扑连通性的（选择）集的连续二元关系被定义为是至关重要的这个问题。在Eilenberg-Sonnenschein（ES）的研究纲领中提到了双向关系，它给出了连通性的四个综合的、完整的刻画，以及它的自然扩展;以及仅仅源于它的两个结果。这六个定理在经济学和数学文献中都是新颖的：它们概括了Eilenberg（1941）、Sonnenschein（1965）、Schmeidler（1971）和Sen（1969）的开创性结果，并且与几个应用背景以及正在进行的理论工作有关。
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.
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