Uniqueness of Cartesian Products of Compact Convex Sets

Volume 59 / 2011

Zbigniew Lipecki, Viktor Losert, Jiří Spurný Bulletin Polish Acad. Sci. Math. 59 (2011), 175-183 MSC: 46A55, 52A07. DOI: 10.4064/ba59-2-7


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 $Y_{b(i)}$, $i\in I$.


  • Zbigniew LipeckiInstitute of Mathematics
    Polish Academy of Sciences
    Wrocław Branch
    Kopernika 18
    51-617 Wrocław, Poland
  • Viktor LosertInstitut für Mathematik
    Universität Wien
    1090 Wien, Austria
  • Jiří SpurnýDepartment of Mathematical Analysis
    Faculty of Mathematics and Physics
    Charles University
    Sokolovská 83
    186 75 Praha 8, Czech Republic

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