Description

• Title:
  On the operator of center of distances between the spaces of closed subsets of the real line
• Creator:
  Bartoszewicz, Artur;
  Filipczak, Małgorzata;
  Horbaczewska, Grażyna;
  Lindner, Sebastian;
  Prus-Wiśniowski, Franciszek
• Description:
  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 $[0,1]$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2023 Artur Bartoszewicz, Małgorzata Filipczak, Grażyna Horbaczewska, Sebastian Lindner, Franciszek Prus-Wiśniowski;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2023.12.31
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 63, No 2 (June 2024); 413 - 427;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/47721/37304 ;https://apcz.umk.pl/TMNA/article/view/47721/37305
• Subject:
  Center of distances;
  Hausdorff metric;
  semicontinuity;
  orbit;
  Cantorval;
  Primary: 54E40;
  Secondary: 47H04, 54E35
• Identifier: https://apcz.umk.pl/TMNA/article/view/47721
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other