(untitled) (Communications in Mathematical Research, 2025)
In this paper we prove that the Gromov-Hausdorff distance between R^n and its subset A is finite if and only if A is an ε-net in 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.