Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

Tom 158 / 2003

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

Streszczenie

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 $\aleph _{0}$.

Autorzy

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