图像拓扑意义下KKM点集的通有稳定性

The Generic Stability of the Set of KKM Points in the Sense of Graph Topology

为了获得在图像拓扑意义下上半连续KKM映射的KKM点集的通有稳定性,即在Baire分类意义下,绝大多数KKM映象的KKM点都是本质的。通过构造上半连续KKM映射G所组成的集合M,并定义M上的KKM映射的图像之间的Hausdorff度量,证明了M是完备度量空间。然后利用usco方法,在证明了M上的KKM点集映射F是紧值上半连续的,从而由Fort定理得到F在M上是通有连续的,即F是通有稳定的。

In this paper,we prove that KKM mappings with upper semicontinuous are generic stability with respect to the graph topology,i. e,in the sense of Baire category,for most KKM mappings,all their KKM points are essential. First,we define a Hausdorff- metric space M consisted of all upper semicontinuous KKM mappings,and prove that M is a complete metric space. Then we denote by F（ G） the set of all KKM points of G,using of usco approach,and prove that F is compact and upper semicontinuous,therefore,obtain that F is generic stability on M by use of Fort theorem.