On Pliś metric on the space of strictly convex compacta
Dusan D. Repovs, Maxim Viktorovich Balashov · Journal of convex analysis · 2011
We consider a certain metric on the space of all convex compacta in ▫$\mathbb{R}^n$▫, introduced by A. Pliś. 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.