On a transversal theorem of Montejano and Karasev

Abstract

We give a new proof of a theorem of Montejano and Karasev regarding $k$-dimensional transversals to small families of convex sets. While their proof uses technical algebraic and topological tools, our proof is a simple application of the Borsuk-Ulam theorem. Additionally, in certain cases our result is stronger than the Montejano-Karasev theorem.

The contents of this manuscript was published as part of the paper: O. Cheong, X. Goaoc, A. F. Holmsen, Some New Results on Geometric Transversals. Discrete Comput Geom (2023)

References in corpus (1)

• Topological transversals to a family of convex sets

Cited by in corpus (1)

• An $({\aleph }_0,k+2)$-Theorem for $k$-Transversals