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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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