@Article{CMR-41-1,
author = {Mikhailov , I.N. and Tuzhilin , A.A.},
title = {When the Gromov-Hausdorff Distance Between Finite-Dimensional Space and Its Subset Is Finite?},
journal = {Communications in Mathematical Research },
year = {2025},
volume = {41},
number = {1},
pages = {1--8},
abstract = {<p style="text-align: justify;">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 $ε &gt; 0.$ 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.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2024-0041},
url = {http://global-sci.org/intro/article_detail/cmr/23926.html}
}