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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142977We 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.12 pagesMetric GeometryDifferential Geometry54E40; 53C70Local Lipschitz property of the map which puts in correspondence to N--net its Chebyshev centertext