论文标题
无限的脂肪凸家家族的有限K-转盘
Finite k-Transversals of Infinite Families of Fat Convex Sets
论文作者
论文摘要
我们证明了一个无限$（P，Q）$ - 用$ k $ -flats穿刺脂肪紧凑型凸的定理。此外，我们开发了一个新的框架，通过该框架，无限$（p，q）$ - 有关紧凑型集的定理和$ k $ -flats可以扩展到其“五颜六色”变体。此外，我们表明存在无限$（p，q）$ - 定理并不一定意味着存在相应的有限$（p，q）$ - 定理。
We prove an infinite $(p,q)$-theorem for piercing fat compact convex sets in $\RR^d$ with $k$-flats. Additionally, we develop a new framework through which infinite $(p,q)$-theorems concerning compact sets and $k$-flats can be extended to their 'colorful' variants. Further, we show that the existence of an infinite $(p,q)$-theorem does not necessarily imply the existence of the corresponding finite $(p,q)$-theorem.
