English

No weak epsilon nets for lines and convex sets in space

Combinatorics 2024-09-06 v3 Metric Geometry

Abstract

We prove that there exist no weak ε\varepsilon-nets of constant size for lines and convex sets in Rd\mathbb{R}^d.

Cite

@article{arxiv.2202.02719,
  title  = {No weak epsilon nets for lines and convex sets in space},
  author = {Otfried Cheong and Xavier Goaoc and Andreas F. Holmsen},
  journal= {arXiv preprint arXiv:2202.02719},
  year   = {2024}
}

Comments

Boris Bukh has informed us that our construction can be extended to 2-flats in $\mathbb{R}^4$. 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)

R2 v1 2026-06-24T09:22:20.705Z