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arXiv · 2605.19680

Contractibility of the space of $\varepsilon$-nets in $\mathbb{R}$

Ivan N. Mikhailov
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Abstract

In this note, we show that the space of all $\varepsilon$-nets in the real line $\mathbb{R}$ with a natural metric, equipped with either Hausdorff or Gromov--Hausdorff distance, is contractible.

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Ivan N. Mikhailov. 2026-05-19. Contractibility of the space of $\varepsilon$-nets in $\mathbb{R}$. https://arxiv.org/abs/2605.19680

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