We give a generalization of dimension independent Helly Theorem of Adiprasito, B\'{a}r\'{a}ny, Mustafa, and Terpai (Discrete & Computational Geometry 2022) to higher dimensional transversal. We also prove some impossibility results that establish the tightness of our extension.

翻译：我们给出了Adiprasito、Bárány、Mustafa和Terpai（《离散与计算几何》2022）的维数无关Helly定理向高维横截的推广。我们还证明了一些不可能性结果，确立了该推广的紧致性。