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Uniqueness of Cartesian products of compact convex sets. (English) Zbl 1236.46009
Let \(X_i\), \(i\in I\), and \(Y_j\), \(j\in J\), be compact convex sets whose Choquet boundaries are affinely independent, and let \(\phi\) be an affine homeomophism of \(\prod_{i\in I}X_i\) and \(\prod_{j\in J}Y_j\). Then there is a bijection \(b: I\to J\) such that \(\phi\) is the product of some affine homeomorphisms of \(X_i\) onto \(Y_{b(i)}\), \(i\in I\).

MSC:
46A55 Convex sets in topological linear spaces; Choquet theory
52A07 Convex sets in topological vector spaces (aspects of convex geometry)
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