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

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.

arXiv commentThe title has been changed, and this version substantially simplifies the arguments from the previous version. 8 pages, 2 figures