广义KKM映射的通有稳定性及本质连通区的存在性

The Generic Stability of Generalized KKM Mapping and the Existence of Essential Component

讨论广义KKM映像的通有稳定性及一定条件下本质连通区的存在性,又在杨彦龙的基础上讨论了比其更一般的空间上的广义KKM映像的通有稳定性,并得到了广义KKM映像一定条件下本质连通区的存在性定理。证明了在由广义KKM映像构成的M中,存在一个稠密剩余集Q,使得广义KKM映像的点集映射在Q上是连续的,从而是通用稳定的,并且在适当条件下由广义KKM映像构成的M′中至少存在一个本质连通区。

It discusses the generic stability of generalized KKM mapping and the existence of essential component in certain conditions.Further,based on bibliography Yang yan-long,the paper discusses the generic stability of generalized KKM mapping in more general space and proves the theorem of essential component existence of generalized KKM mapping in certain conditions.The conclusion in the paper is that there exists a dense residual Q in space M and in Q,the point set mapping is continuous and generically stable.Besides,in certain conditions there is at least one essential component in constituted by the generalized KKM mapping.