On the number of minimal pairs of compact convex sets that are not translates of one another
Volume 158 / 2003
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 $\aleph _{0}$.
