论文标题
巴拉赫空间的星际覆盖物
Star-finite coverings of Banach spaces
论文作者
论文摘要
我们研究无限维规范空间的星际覆盖物。如果其每个成员都只有有限的其他许多家庭成员，则一组套装被称为星际仪式。随之而来的是我们的结果是，LUR或均匀的Fréchet光滑无限二维Banach空间不会通过封闭的球允许恒星覆盖物。另一方面，我们提供了一个非常涉及的构造，证明存在$ C_0（γ）$的星形覆盖物，由Fréchet光滑中心对称框架凸面。一个类似但更简单的结构表明，每个可数尺寸的规范空间（因此不完整）都有一个恒星覆盖的封闭球。
We study star-finite coverings of infinite-dimensional normed spaces. A family of sets is called star-finite if each of its members intersects only finitely many other members of the family. It follows by our results that an LUR or a uniformly Fréchet smooth infinite-dimensional Banach space does not admit star-finite coverings by closed balls. On the other hand, we present a quite involved construction proving existence of a star-finite covering of $c_0(Γ)$ by Fréchet smooth centrally symmetric bounded convex bodies. A similar but simpler construction shows that every normed space of countable dimension (and hence incomplete) has a star-finite covering by closed balls.
