The mapping of compact into the set of its Chebyshev centres is Lipschitz in the space l^n_{\infty}

Details The mapping of compact into the set of its Chebyshev centres is Lipschitz in the space l^n_{\infty} The mapping of compact into the set of its Chebyshev centres is Lipschitz in the space l^n_{\infty}

2006-09-08

arxiv.org/abs/math/0609229v6

Mathematics

Metric Geometry

8 pages

Scientific paper

In this article the authors prove strong stability of the set of all
Chebyshev centres of the bounded closed subset of the metric space. We endow
the set of all compacts of the space $l^n_{\infty}$ with Hausdorff metric and
prove that the map which puts in correspondence to each compact of
$l^n_{\infty}$ the set of its Chebyshev centres is Lipshitz.

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