Year: 2025
Author: I.N. Mikhailov, A.A. Tuzhilin
Communications in Mathematical Research , Vol. 41 (2025), Iss. 1 : pp. 1–8
Abstract
In this paper we prove that the Gromov-Hausdorff distance between $\mathbb{R}^n$ and its subset $A$ is finite if and only if $A$ is an $ε$-net in $\mathbb{R}^n$ for some $ε > 0.$ For infinite-dimensional Euclidean spaces this is not true. The proof is essentially based on upper estimate of the Euclidean Gromov-Hausdorff distance by means of the Gromov-Hausdorff distance.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2024-0041
Communications in Mathematical Research , Vol. 41 (2025), Iss. 1 : pp. 1–8
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Metric space $ε$-net Gromov-Hausdorff distance.