有界凸集空间中的几乎同时唯一远达子集

On Almost Simultaneous Uniquel Remotel Sets with Respect to Bounded Convex Subsets

研究了有界凸集关于一般有界闭集的同时远达点的存在唯一性问题．在集合的Hausdorff距离下，引进了有界集空间中的几乎同时唯一远达了集的概念，证明了各向一致凸（自反局部一致凸）Banach空间中的任何有界闭子集都是关于有界凸集（紧凸集）的几乎同时唯一远达子集，从而使M·Edelstein定理、E·Asplund定理在集合空间得到了多元推广．

In this paper, we study the existence and uniqueness of simultaneous farthest points to bounded convex subsets from general bounded closed subsets.Under the Hausorff metric of sets,we define the concept of almost simultaneous uniquely remotel set with respect to bounded subsets.It is proved that in an uniform convex in every direction (a reflexive locally uniformly convex) Banach space X,every bounded closed subset of X is an almost simultaneous uniquely farthest subset with respect to bounded (compact) convex subsets of X,these result obtained are a multivalued version of theorems due to M.Edelstein and E.Asplund.