Abstract
We show that every finite-dimensional Alexandrov space X with curvature bounded from below embeds canonically into a product of an Alexandrov space with the same curvature bound and a Euclidean space such that each affine function on X comes from an affine function on the Euclidean space.
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Acknowledgements
We would like to thank Vitali Kapovitch, Alexander Lytchak and Anton Petrunin for comments and discussions on different aspects of Alexandrov geometry. We would also like to thank the anonymous referee for his remarks that helped to improve the exposition. The first named author was partly supported by a ‘Kurzzeitstipendium für Doktoranden’ by the German Academic Exchange Service (DAAD).
