一般拓扑空间上的KKM定理,匹配定理,重合点定理  

KKM Theorem,Matching Theorems,Coincidence Theorems on General Topological Spaces

作　　者：朴勇杰[1] 

机构地区：[1]延边大学理学院数学系,延吉133002

出　　处：《应用泛函分析学报》2011年第1期85-90,共6页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(10361005);延边大学科研项目(2008[8号])

摘　　要：引进没有任何凸结构的拓扑空间上的广义R-KKM映射的定义,并利用古典的KKM原理得到一般拓扑空间上的KKM型定理,然后利用该结果得到Lassonde型匹配定理和Klee型相交定理,最后作为应用给出非紧的拓扑空间上不动点定理和重合点存在定理.推广和改进了文献中的相应结果.Our aim in this paper is to introduce the definition of generalized R-KKM mapping in general topological space without any convexity structure and use the classical KKM pronciple to obtain KKM type theorems on general topological spaces, and then from which, we obtain matching theorems in the sense of Lassonde and an intersection theorem in the sense of Klee, finally we give fixed point theorem and coincidence point theorems on non-compact topological spaces. Our main results generalize and improve the corresponding results in the recent literatures.

关 键 词：R-KKM映射 R-子集 上半连续 下半连续 匹配 重合点 

分 类 号：O189.1[理学—数学] O177.91[理学—基础数学]