度量空间中两集间距离的可达性和唯一性

The Reachability and Uniqueness of Distance Between Two Sets in Metric Spaces

本文讨论了度量空间中两集间距离的可达性与唯一性问题。得到,在一致凸Banach空间中,当A为紧子集,B为闭凸子集时,A、B间的距离可达,又当A为紧凸集且具有相对于B的局部严格凸性,D(A,B)>0时,不仅距离可达。

In this paper we discuss the reachability and uniqueness of distance between two sets in metric spaces.In uniformly convex Banach spaces we conclude that the distance between sets A and B is reachable if set A is compact and B is closed convex.Moreover, if set A is compact and locally strict convex with respect to set B while D(A,B)>0,the distance between sets A and B in not only reachable but also unique