拓扑空间中的KKM型定理和重合点定理.pdf

Journal of Mathematical Research Exposition May, 2008, Vol.28, No.2, pp.403–412 DOI:10.3770/j.issn:1000-341X.2008.02.022 Http:// KKM Type Theorems and Coincidence Theorems in Topological Spaces 1 2 ZHENG Lian , DING Xie Ping (1. Department of Mathematics, Yangtze Normal University, Chongqing 408100, China; 2. Department of Mathematics, Sichuan Normal University, Sichuan 610066, China) (E-mail: zhenglian66@) Abstract A class of finitely continuous topological spaces (in short, FC-spaces) is introduced. Some new KKM type theorems and coincidence theorems involving admissible set-valued map- pings and the set-valued mapping with compactly local intersection property are proved in FC- spaces. As applications, some new fixed point theorems are obtained in FC-spaces. These theorems improve and generalize many known results in recent literature. Keywords FC-space; KKM type theorem; coincidence theorem; admissible set-valued map; compactly local intersection property. Document code A MR(2000) Subject Classification 54H25; 54C60 Chinese Library Classification O177.92 1. Introduction In 1987, Horvath[1], replacing convex hulls by contractible sets, gave a purely topological version of the KKM theorem. Since then, Park and Kim[2] introduced the concepts of admissible set-valued mappings and generalized convex (or G-convex) spaces. Verma [3] introduced the concepts of G-H-convex spaces. Ben-El-Mechaiekh et.al [4] introduced the concepts of L-convex spaces. They established some KKM type theorems in these spaces respectively. L-convex space includes all the above abstract convex spaces as special cases. Ding[5] p