论文标题
Borsuk在公制空间中的问题
Borsuk's Problem in Metric Spaces
论文作者
论文摘要
在1933年，K。Borsuk提出了以下问题：可以将$ \ Mathbb {e}^n $中的每个有限设置分为$ n+1 $ thimel直径的子集吗？ 1965年，V。G。Boltyanski和I. T. Gohberg做出了以下猜想：$ n $二维公制空间中的每个有限设置都可以分为$ 2^n $较小直径的子集。在本文中，我们证明了以下结果：$ n $维度中的每个有限集可以将$ 2^{n}（（n+1）\ log（n+1）+（n+1）+（n+1）\ log \ log \ log \ log \ log \ log（n+1）+5n+5n+5）+5n+5）$较小的字符的子集。
In 1933, K. Borsuk proposed the following problem: Can every bounded set in $\mathbb{E}^n$ be divided into $n+1$ subsets of smaller diameters? In 1965, V. G. Boltyanski and I. T. Gohberg made the following conjecture: Every bounded set in an $n$-dimensional metric space can be divided into $2^n$ subsets of smaller diameters. In this paper, we prove the following result: Every bounded set in an $n$-dimensional metric space can be divided into $2^{n}((n+1)\log (n+1)+(n+1)\log \log (n+1)+5n+5)$ subsets of smaller diameters.
