Uniqueness of Cartesian Products of Compact Convex Sets

Zbigniew Lipecki, Viktor Losert, and Jiří Spurný. "Uniqueness of Cartesian Products of Compact Convex Sets." Bulletin of the Polish Academy of Sciences. Mathematics 59.2 (2011): 175-183. <http://eudml.org/doc/281284>.

@article{ZbigniewLipecki2011,
abstract = {Let $X_i$, i∈ I, and $Y_j$, j∈ J, be compact convex sets whose sets of extreme points are affinely independent and let φ be an affine homeomorphism of $∏_\{i∈ I\} X_i$ onto $∏_\{j∈ J\} Y_j$. We show that there exists a bijection b: I → J such that φ is the product of affine homeomorphisms of $X_i$ onto $Y_\{b(i)\}$, i∈ I.},
author = {Zbigniew Lipecki, Viktor Losert, Jiří Spurný},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {compact convex set; simplex; extreme point; affine independence; affine homeomorphism; Cartesian product; Choquet boundary},
language = {eng},
number = {2},
pages = {175-183},
title = {Uniqueness of Cartesian Products of Compact Convex Sets},
url = {http://eudml.org/doc/281284},
volume = {59},
year = {2011},
}

TY - JOUR
AU - Zbigniew Lipecki
AU - Viktor Losert
AU - Jiří Spurný
TI - Uniqueness of Cartesian Products of Compact Convex Sets
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2011
VL - 59
IS - 2
SP - 175
EP - 183
AB - Let $X_i$, i∈ I, and $Y_j$, j∈ J, be compact convex sets whose sets of extreme points are affinely independent and let φ be an affine homeomorphism of $∏_{i∈ I} X_i$ onto $∏_{j∈ J} Y_j$. We show that there exists a bijection b: I → J such that φ is the product of affine homeomorphisms of $X_i$ onto $Y_{b(i)}$, i∈ I.
LA - eng
KW - compact convex set; simplex; extreme point; affine independence; affine homeomorphism; Cartesian product; Choquet boundary
UR - http://eudml.org/doc/281284
ER -