On the Existence of Greatest and Maximal Elements

Haishu Lu
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Abstract

The main purpose of this paper is to deal with the existence of greatest and maximal elements of weak and strict preference relations and give necessary conditions for the existence of greatest and maximal elements of weak and strict preference relations in framework of general topological spaces without linear and convex structure. The well known KKM theorem is applied to proving the existence theorem of greatest and maximal elements of weak and strict preference relations under mild conditions.
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论极大元与极大元的存在性
本文的主要目的是在无线性和凸结构的一般拓扑空间框架下,研究弱偏好关系和严格偏好关系的最大元素和最大元素的存在性问题,并给出了弱偏好关系和严格偏好关系的最大元素和最大元素存在的必要条件。应用著名的KKM定理,证明了弱偏好关系和严格偏好关系在温和条件下最大元和极大元的存在性定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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