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arXiv · 2402.10012

A geometric proof of the infinite $(p, q)$-theorem for hyperplane piercing

Sutanoya Chakraborty·Arijit Ghosh·Soumi Nandi
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Abstract

We provide a geometric proof of the $(\aleph_{0}, d+1)$-theorem for piercing compact connected sets by hyperplanes. Our argument uses only elementary properties of convex sets and clarifies the core geometric structure behind the theorem.

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Sutanoya Chakraborty, Arijit Ghosh, Soumi Nandi. 2025-09-08. A geometric proof of the infinite $(p, q)$-theorem for hyperplane piercing. https://arxiv.org/abs/2402.10012

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