On Pli\'{s} metric on the space of strictly convex compacta
  We consider a certain metric on the space of all convex compacta in $\R^{n}$, 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. 
Maxim V. Balashov and Du\v{s}an Repov\v{s}
math.GN math.MG