Uniqueness of Cartesian Products of Compact Convex Sets

摘要

Summary. 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.