Approximation of completely bounded sets by the deep holes method. (Q1395176)

This paper is devoted to the deep holes method (DHM), which is a universal adaptive iteration method for the approximation of completely bounded sets in arbitrary metric spaces. The method is based on the construction of nearly optimal metric \(\varepsilon\)-nets and \(\varepsilon\)-distinguishable subsets. For a prescribed cardinality of a metric \(\varepsilon\)-net, the DHM is shown to construct an approximation, with the radius of the covering balls being, at most, twice as large as the minimum possible radius. Ref. 12 in number