论文标题
通过Borsuk编号来计算Gromov-Hausdorff距离
Calculating Gromov-Hausdorff Distance by means of Borsuk Number
论文作者
论文摘要
本文的目的是证明Gromov-Hausdorff距离的属性与Borsuk猜想之间的联系。给定有限度量空间$ x $的BORSUK数量是$ n $的基数$ x $，因此可以将$ x $划分为$ n $较小的零件（就直径而言）。在一个空间的直径和基数分别小于另一个空间的直径和基数小于另一个空间的直径和基数，获得了有界度量空间之间的gromov-hausdorff距离的确切公式。利用培根在卢斯托尼克 - 雪尼雷尔曼和波尔斯克问题之间的等效结果，获得了几种推论。
The purpose of this article is to demonstrate the connection between the properties of the Gromov--Hausdorff distance and the Borsuk conjecture. The Borsuk number of a given bounded metric space $X$ is the infimum of cardinal numbers $n$ such that $X$ can be partitioned into $n$ smaller parts (in the sense of diameter). An exact formula for the Gromov--Hausdorff distance between bounded metric spaces is obtained under the assumption that the diameter and cardinality of one space are less than the diameter and Borsuk number of another, respectively. Using the results of Bacon's equivalence between the Lusternik--Schnirelmann and Borsuk problems, several corollaries are obtained.
