Uniqueness of Cartesian Products of Compact Convex Sets

• Autorzy: Zbigniew Lipecki , Viktor Losert , Jiří Spurný
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46A55: Convex sets in topological linear spaces; Choquet theory
• 52A07: Convex sets in topological vector spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: 59
• Numer: 2
• Strony: 175-183

Daty

wydano

2011

Twórcy

autor

Zbigniew Lipecki

• Institute of Mathematics, Polish Academy of Sciences, Wrocław Branch, Kopernika 18, 51-617 Wrocław, Poland

autor

Viktor Losert

• Institut für Mathematik, Universität Wien, 1090 Wien, Austria

autor

Jiří Spurný

• Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/ba59-2-7