不相交球的线横截
Line transversals to disjoint balls
摘要：
证明了$R^3$中三个不相交球按给定顺序相交的直线的方向集是$S^2$的严格凸子集。然后，我们将这个结果推广到$R^d$中的$n$不相交球。因此，我们可以改进几个旧的和新的结果线横截到任意维不相交的球，如界限上的数量的连通组件和Helly型定理。
英文摘要：
We prove that the set of directions of lines intersecting three disjoint balls in $R^3$ in a given order is a strictly convex subset of $S^2$. We then generalize this result to $n$ disjoint balls in $R^d$. As a consequence, we can improve upon several old and new results on line transversals to disjoint balls in arbitrary dimension, such as bounds on the number of connected components and Helly-type theorems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
