论文标题
Borsuk的分区问题四维$ \ ell_ {p} $ space
Borsuk's partition problem in four-dimensional $\ell_{p}$ space
论文作者
论文摘要
1933年，Borsuk猜想，每个$ n $维限制的套件都可以分为$ n+1 $较小直径的子集。到目前为止，问题仍然以$ 4 \ leq n \ leq 63 $开放。在本文中，我们首先讨论了$ n $维的立方体与$ \ ell_ {p} $ ball $（1 \ leq p <2）$之间的Banach-Mazur距离，然后我们研究了通用的Borsuk Borsuk的分区问题，在公制空间中的borsuk分区问题，并证明所有限制的$ x $ $ x $ $ x $ $ x $ $ x $ $ \ ell \ ell_ el \ ell_ el \ ell_ el \ ell_ p} p} 直径。
In 1933, Borsuk made a conjecture that every $n$-dimensional bounded set can be divided into $n+1$ subsets of smaller diameter. Up to now, the problem is still open for $4\leq n\leq 63$. In this paper, we firstly discuss the Banach-Mazur distance between the $n$-dimensional cube and the $\ell_{p}$ ball $(1\leq p< 2)$, then we study the generalized Borsuk's partition problem in metric spaces and prove that all bounded sets $X$ in every four-dimensional $\ell_{p}$ space can be divided into $2^4$ subsets of smaller diameter.
