Uniqueness of Cartesian Products
 of Compact Convex Sets

Zbigniew Lipecki; Viktor Losert; Jiří Spurný

doi:10.4064/ba59-2-7

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Uniqueness of Cartesian Products of Compact Convex Sets

Zbigniew Lipecki ¹ ; Viktor Losert ² ; Jiří Spurný ³

¹ Institute of Mathematics Polish Academy of Sciences Wrocław Branch Kopernika 18 51-617 Wrocław, Poland
² Institut für Mathematik Universität Wien 1090 Wien, Austria
³ Department of Mathematical Analysis Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 2, pp. 175-183.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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

DOI : 10.4064/ba59-2-7

Keywords: compact convex sets whose sets extreme points affinely independent varphi affine homeomorphism prod prod there exists bijection colon varphi product affine homeomorphisms

Affiliations des auteurs :

Zbigniew Lipecki ¹ ; Viktor Losert ² ; Jiří Spurný ³

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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) no. 2, pp. 175-183. doi : 10.4064/ba59-2-7. http://geodesic.mathdoc.fr/articles/10.4064/ba59-2-7/

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