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

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.