On the number of minimal pairs of compact convex sets that are not translates of one another

Volume 158 / 2003

J. Grzybowski, R. Urbański Studia Mathematica 158 (2003), 59-63 MSC: 52A07, 26A27. DOI: 10.4064/sm158-1-5

Abstract

Let $[A,B]$ be the family of pairs of compact convex sets equivalent to $(A,B)$. We prove that the cardinality of the set of minimal pairs in $[A,B]$ that are not translates of one another is either 1 or greater than $\aleph _{0}$.

Authors

  • J. GrzybowskiFaculty of Mathematics and Computer Science
    Adam Mickiewicz University
    Umultowska 87
    61-614 Poznań, Poland
    e-mail
  • R. UrbańskiFaculty of Mathematics and Computer Science
    Adam Mickiewicz University
    Umultowska 87
    61-614 Poznań, Poland
    e-mail

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