KKM定理中无限交集的紧性及其应用  

The compactness of the infinite intersection in KKM theorem and its applications

作　　者：王元恒 李雪婷 WANG Yuanheng;LI Xueting(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学数学与计算机科学学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2022年第2期147-152,共6页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(12171435)。

摘　　要：在原有条件不变的情况下,证明了著名的KKM定理中的无限交集不但非空,而且还是闭集、紧集,并给出了KKM定理中的一些交集结构.此外,作为应用,给出了抽象变分不等式解集的闭性、紧性、凸紧性、存在唯一性和解的特征性定理.其结果推广和改进了著名的KKM定理、Minty引理和其他许多相应的抽象变分不等式的结果.Under the original conditions,it was proved that the infinite intersection in the famous KKM theorem was not only non-empty,but also closed and compact,some intersection structures in KKM theorem were given.Furthermore,as its applications,some results about the closeness,the compactness,the convexity,the uniqueness and the structure theorems of the solution set of the abstract variational inequalities were presented.The results generalized and improved the famous KKM theorem,Minty lemma and many other related results of the abstract variational inequality.

关 键 词：KKM定理 凸性 紧性 抽象变分不等式 解的存在唯一性 

分 类 号：O177.91[理学—数学]