A geometric proof of the infinite $(p, q)$-theorem for hyperplane piercing
Sutanoya Chakraborty, Arijit Ghosh, Soumi Nandi
Published: 2024/2/15
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.