Banach空间的球覆盖性质

Ball-covering property of Banach spaces

如果Banach空间X的单位球面可以被可数个不包含原点的球所构成的球族所覆盖,则称X具有球覆盖性质.本文对Banach空间的球覆盖性质这个研究方向的发展进行简要回顾,同时也给出一些新的相关研究成果.

A Banach space admitting a unit sphere covering consisting of countably many balls off the origin is said to have ball-covering property. In this paper, we present a brief review on the research area of ball-covering property of Banach spaces, and some new results about this topic are included.