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 ℵ₀.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-1-5,
author = {J. Grzybowski and R. Urba\'nski},
title = {On the number of minimal pairs of compact convex sets that are not translates of one another},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {59-63},
zbl = {1041.52003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-1-5}
}
J. Grzybowski; R. Urbański. On the number of minimal pairs of compact convex sets that are not translates of one another. Studia Mathematica, Tome 157 (2003) pp. 59-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-1-5/