On the operator of center of distances between the spaces of closed subsets of the real line
DOI:
https://doi.org/10.12775/TMNA.2023.023Keywords
Center of distances, Hausdorff metric, semicontinuity, orbit, CantorvalAbstract
We study properties of an operator $S$ which assigns to compact subsets of $[0,1]$ their centers of distances. We consider its continuity points and its upper semicontinuity points as well as 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 $[0,1]$.References
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Copyright (c) 2023 Artur Bartoszewicz, Małgorzata Filipczak, Grażyna Horbaczewska, Sebastian Lindner, Franciszek Prus-Wiśniowski
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
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