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Uniqueness of Cartesian Products of Compact Convex Sets

Zbigniew Lipecki, Viktor Losert, Jiří Spurný (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

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