On the operator of center of distances between the spaces of closed subsets of the real line - Bartoszewicz, Artur; Filipczak, Małgorzata; Horbaczewska, Grażyna; Lindner, Sebastian; Prus-Wiśniowski, Franciszek (Topological Methods in Nonlinear Analysis, 2023)
We study properties of an operator $S$ which assigns to compact subsetsof $[0,1]$ their centers of distances.We consider its continuity points and its upper semicontinuity points as wellas orbits and fixed points of this operator. We also compute centers of distances of some classic sets. Using properties of operator $S$ we show that the family of achievement sets is of the first category in the space of compact subsets of $[0,1]$.