A problem of intersection of balls in normed space

D. A. Ilyukhin

A problem of intersection of balls in normed space

Metric Geometry 2026-06-25 v1

Authors: D. A. Ilyukhin

Abstract

This paper investigates the topological properties of intersections of balls in finite-dimensional normed spaces - a problem that naturally arises when constructing covers for estimating the Gromov-Hausdorff distance. We study the topology of a set obtained by removing a large closed ball from a finite intersection of small open balls. It is proved that in an arbitrary normed plane, such a set is always contractible, provided that it is non-empty.

Keywords

normed spaces intersection of balls contractible gromov-hausdorff distance topology finite-dimensional

Cite

@article{arxiv.2606.27583,
  title  = {A problem of intersection of balls in normed space},
  author = {D. A. Ilyukhin},
  journal= {arXiv preprint arXiv:2606.27583},
  year   = {2026}
}

Comments

8 pages, 2 figures