Local Lipschitz property of the map which puts in correspondence to N--net its Chebyshev center

Details Local Lipschitz property of the map which puts in correspondence to N--net its Chebyshev center Local Lipschitz property of the map which puts in correspondence to N--net its Chebyshev center

2005-09-13

arxiv.org/abs/math/0509275v4

Mathematics

Metric Geometry

12 pages

Scientific paper

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

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