A subset A of finite-dimensional Euclidean space has finite Gromov-Hausdorff distance to the whole space if and only if A is an epsilon-net for some epsilon.
Memoli, Gromov-Hausdorff distances in Euclidean spaces , in IEEE Computer Society Confer- ence on Computer Vision and Pattern Recognition Workshops, June (2008), pp
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When the Gromov-Hausdorff distance between finite-dimensional space and its subset is finite?
A subset A of finite-dimensional Euclidean space has finite Gromov-Hausdorff distance to the whole space if and only if A is an epsilon-net for some epsilon.