Let , i∈ I, and , j∈ J, be compact convex sets whose sets of extreme points are affinely independent and let φ be an affine homeomorphism of onto . We show that there exists a bijection b: I → J such that φ is the product of affine homeomorphisms of onto , i∈ I.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-2-7,
author = {Zbigniew Lipecki and Viktor Losert and Ji\v r\'\i\ Spurn\'y},
title = {Uniqueness of Cartesian Products of Compact Convex Sets},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {59},
year = {2011},
pages = {175-183},
zbl = {1236.46009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-2-7}
}
Zbigniew Lipecki; Viktor Losert; Jiří Spurný. Uniqueness of Cartesian Products of Compact Convex Sets. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) pp. 175-183. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-2-7/