摘要
考虑如下问题:对一个Banach空间X,已知其单位球面SX可以被n+1个不含原点为其内点的闭球所覆盖,则其最小覆盖半径是多少?本文针对一特殊空间Rn,首先证明了在Rn中,若有一点集{xi}im=1满足一定条件,则可给出一特殊的球覆盖,且此覆盖的半径即为最小半径.进一步本文还给出了在Rn中若任意给定r≥32,可找到一个以r为覆盖半径的球覆盖,且此覆盖的势为极小的.
Considering the following problem： for a Banach space X with dim X= n,it has already known that the sphere of the unit ball of X can be covered by a ball-covering of n＋ 1 closed balls not containing the origin in its interior,then what is its smallest radius？ This article first proves that there exists a specific ball-covering with the smallest radius in R＂ if a set {xi}i=1^m satisfying some given term,then presents a minimal ball-covering with arbitrary given r≥√3/2 as its radius.
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
2006年第5期621-623,共3页
Journal of Xiamen University：Natural Science
