MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Local Lipschitz property for the Chebyshev center mapping over $N$-nets
Pyotr N. Ivanshin and Evgenii N. Sosov

Abstract

We prove local Lipschitz property of the map which puts in correspondence to each exact $N$-net its Chebyshev center. If dimension of Euclidean or Lobachevsky space is greater than $1$ and the net consists of more than $2$ points we show that this map is not Lipschitz in a neighbourhood of the space of all $2$-nets embedded into the space of $N$-nets endowed with Hausdorff metric.

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Keywords: Chebyshev center; local Lipschitz property; $N$-net; Hausdorff metric.

MSC: 54E40, 52C35

Pages:  9--22     

Volume  60 ,  Issue  1 ,  2008