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 anε-net in R^(n)for somε>0.For infinite-dimensional Euclidean spaces this is not true.The proo...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 anε-net in R^(n)for somε>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.展开更多
基金supported by the National Key R&D Program of China(Grant No.2020YFE0204200).
文摘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 anε-net in R^(n)for somε>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.
