Local Lipschitz property for the Chebyshev center mapping over $N$-nets

Authors

  • Pyotr N. Ivanshin N.G. Chebotarev's RIMM, Kazan State University, 420008, Kazan, Universitetskaya, 17, Russia Author
  • Evgenii N. Sosov N.G. Chebotarev's RIMM, Kazan State University, 420008, Kazan, Universitetskaya, 17, Russia Author

Keywords:

Chebyshev center, local Lipschitz property, $N$-net, Hausdorff metric

Subjects:

54E40, 52C35

Abstract

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

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Published

2008-01-15

Issue

Vol. 60 No. 1 (2008): Vol. 60, Issue 1

Section

Articles

License

Copyright (c) 2008 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.