拓扑空间中的KKM型定理和重合点定理

KKM Type Theorems and Coincidence Theorems in Topological Spaces

中文关键词:  $FC$-空间  KKM型定理  重合点定理  容许类集值映射  紧局部交性质.

英文关键词:$FC$-space  KKM type theorem  coincidence theorem  admissible set-valued map  compactly local intersection property.

中文摘要:

      引入了一类新的有限连续空间(简称, $FC$-空间),并在$FC$-空间中证明了一些新的涉及容许类集值映射和具有紧局部交性质的KKM型定理和重合点定理.作为应用,在$FC$-空间中得到了一些新的不动点定理.这些结果统一和推广了近期文献在抽象凸空间中的一些重要结果.

英文摘要:

      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 mappings 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.