论文标题
五颜六色的古德曼 - 帕拉克·温格定理
A colorful Goodman-Pollack-Wenger theorem
论文作者
论文摘要
Hadwiger的横向定理为在平面中的成对分离式凸的家族横向存在提供了必要和足够的条件。随后将这些条件推广到超平面横向到Goodman，Pollack和Wenger的$ \ Mathbb {r}^d $中的凸的一般家庭。在这里，我们展示了其定理的丰富多彩谱系，证实了Arocha，Bracho和Montejano的猜想。证明是拓扑结构，并使用Borsuk-ulam定理。
Hadwiger's transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These conditions were subsequently generalized to hyperplane transversals to general families of convex sets in $\mathbb{R}^d$ by Goodman, Pollack, and Wenger. Here we show a colorful genealization of their theorem which confirms a conjecture of Arocha, Bracho, and Montejano. The proof is topological and uses the Borsuk-Ulam theorem.
