Uniqueness of Cartesian Products of Compact Convex Sets
Volume 59 / 2011
Bulletin Polish Acad. Sci. Math. 59 (2011), 175-183
MSC: 46A55, 52A07.
DOI: 10.4064/ba59-2-7
Abstract
Let $X_i$, $i\in I$, and $Y_j$, $j\in J$, be compact convex sets whose sets of extreme points are affinely independent and let $\varphi$ be an affine homeomorphism of $\prod_{i\in I} X_i$ onto $\prod_{j\in J} Y_j$. We show that there exists a bijection $b\colon I \to J$ such that $\varphi$ is the product of affine homeomorphisms of $X_i$ onto $Y_{b(i)}$, $i\in I$.
