This article is cited in 4 papers

Relative $N$-radius of a bounded subset of a metric space

E. N. Sosov

Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University

Abstract: 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.

UDC: 515.124.4

Received: 02.03.2011