English

On Pli\'{s} metric on the space of strictly convex compacta

General Topology 2011-12-20 v1 Metric Geometry

Abstract

We consider a certain metric on the space of all convex compacta in Rn\R^{n}, introduced by A. Pli\'s. The set of strictly convex compacta is a complete metric subspace of the metric space of convex compacta with respect to this metric. We present some applications of this metric to the problems of set-valued analysis, in particular we estimate the distance between two compact sets with respect to this metric and to the Hausdorff metric.

Keywords

Cite

@article{arxiv.1112.4166,
  title  = {On Pli\'{s} metric on the space of strictly convex compacta},
  author = {Maxim V. Balashov and Dušan Repovš},
  journal= {arXiv preprint arXiv:1112.4166},
  year   = {2011}
}