Geodesic
Relative $N$-radius of a bounded subset of a metric space
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 4, pp. 28-36

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In the present paper, we study properties of the best radius of approximation of a bounded subset of a metric space by $N$-nets from another set. We obtain an upper bound of the difference of such radii using the Hausdorff distances between the sets under consideration. In the case of bounded metric spaces, the Gromov–Hausdorff distances and a more simple (in terms of amount of calculations) distance between these spaces are used for estimation.
Keywords: metric space, relative $N$-radius, Hausdorff pseudometric, Gromov–Hausdorff distance. 
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     author = {E. N. Sosov},
     title = {Relative $N$-radius of a~bounded subset of a~metric space},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {28--36},
     publisher = {mathdoc},
     volume = {153},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2011_153_4_a2/}
}
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E. N. Sosov. Relative $N$-radius of a bounded subset of a metric space. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 4, pp. 28-36. http://geodesic.mathdoc.fr/item/UZKU_2011_153_4_a2/