Contractibility of the space of $\varepsilon$-nets in $\mathbb{R}$
Metric Geometry
2026-05-20 v1
Abstract
In this note, we show that the space of all -nets in the real line with a natural metric, equipped with either Hausdorff or Gromov--Hausdorff distance, is contractible.
Cite
@article{arxiv.2605.19680,
title = {Contractibility of the space of $\varepsilon$-nets in $\mathbb{R}$},
author = {Ivan N. Mikhailov},
journal= {arXiv preprint arXiv:2605.19680},
year = {2026}
}
Comments
5 pages