FC-空间中的KKM型定理的形式和应用

作为古典KKM定理的推广，Park在他的工作中介绍了G-凸空间和G—KKM映像．最近，Ding介绍了没有任何凸性结构的有限连续拓扑空间（简称FC-空间）的概念，它包含了C-空间（或H-空间）、G-凸空间、L-凸空间等许多具有抽象凸性结构的拓扑空间作为特例，并证明了FC-空间中的KKM型定理．作为改进和推广，作者在FC-空间中讨论了KKM型定理的一些形式，并获得了FC-空间中Ky Fan型sup inf sup形式不等式和一类极大极小不等式．

On a Form of KKM Type Principle and Application in FC-convex Space

As generalizations of the KKM theorem,Park introduced the concept of G-convex space and G-KKM mapping in his works.Ding introduced the concept of finitely continuous topological space(in short FC-space) without any convexity assumptions.FC-sapces include C-space(or H-space),G-convex spaces,L-convex spaces and many topological spaces with abstrcat convexity structure as special cases.Consequently,a KKM type theorem in FC-spaces is proved by Ding.In this paper,using the KKM type theorem,the author gives a form of KKM type theorems and obtains sup inf sup inequalities of Ky Fan type and a class of minimax inequality in FC-space.