无穷维赋范线性空间上的填球问题（英文）

A Packing Problem on Infinite-dimensional Normed Linear Spaces

受Riesz引理及一个有趣问题"无穷维赋范线性空间上的闭单位球是否可以由有限个开单位球覆盖"的启发,本文得到一个有用的结果,利用这个结果可以给出Kottman定理的一个简单证明及填球数的上界估计.并藉由上界估计考虑了L^p(Ω空间上的填球问题.

Motivated by Riesz Lemma and an interesting question, whether a closed unit ball in an infinite-dimensional normed linear space can be covered by finitely many open unit balls, we obtain a useful result which leads to a novel proof of Kottman Theorem and an upper estimate for infinitely-packing numbers. The latter application also stimulates us to propose a packing problem which we consider in the space Lp （Ω）.