2024 On the operator of center of distances between the spaces of closed subsets of the real line
Artur Bartoszewicz, Małgorzata Filipczak, Grażyna Horbaczewska, Sebastian Lindner, Franciszek Prus-Wiśniowski
Topol. Methods Nonlinear Anal. 63(2): 413-427 (2024). DOI: 10.12775/TMNA.2023.023

Abstract

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 $[0,1]$.

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Artur Bartoszewicz. Małgorzata Filipczak. Grażyna Horbaczewska. Sebastian Lindner. Franciszek Prus-Wiśniowski. "On the operator of center of distances between the spaces of closed subsets of the real line." Topol. Methods Nonlinear Anal. 63 (2) 413 - 427, 2024. https://doi.org/10.12775/TMNA.2023.023

Information

Published: 2024
First available in Project Euclid: 17 July 2024

Digital Object Identifier: 10.12775/TMNA.2023.023

Keywords: Cantorval , Center of distances , Hausdorff metric , Orbit , semicontinuity

Rights: Copyright © 2024 Juliusz P. Schauder Centre for Nonlinear Studies

Vol.63 • No. 2 • 2024
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