不完全偏好下的极大元存在定理及其应用

Existence theorems of maximal elements in the sense of incomplete preference and applications

首先提出了不完全偏好的概念 ,发现了不完全偏好与半序之间的关系 .然后 ,将这种关系和拓扑学中的一些原理相结合 ,并利用 Zorn引理得到了许多不完全偏好下的极大元存在定理 ,推广了 Brezis- Browder序集一般原理 .作为应用 ,证明了在半序集中取值的紧距离空间上的拟连续函数必有广义极小值 ,这个结果是著名的 Weierstrass定理的改进 .

It first proposes a concept of the incomplete preference and discovers the relations between the incomplete preference and the semi order.Then,uniting the above relations with some principles in topology,by Zorn's lemma many maximal element theorems in the sense of incomplete preference are obtained, and thus Brezis Browder general principle on ordered sets is extended.As applications,it is proved that a quasi continuous function which is defined on a compact metric space and valued in a semiordered set must have a generalized minimal value,which is an improvement of Weierstrass theorem.