Uniqueness of Cartesian products of compact convex sets. (English) Zbl 1236.46009

Lipecki, Zbigniew; Losert, Viktor; Spurný, Jiří

Bull. Pol. Acad. Sci., Math. 59, No. 2, 175-183 (2011).

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 \(Y_{b(i)}\), \(i\in I\).

Reviewer: S. S. Kutateladze (Novosibirsk)

MSC:

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

Keywords:

compact convex set; simplex; extreme point; affine independence; affine homeomorphism; Cartesian product; Choquet boundary