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Lange, Christian; Stadler, Stephan (2018): Affine functions on Alexandrov spaces. In: Mathematische Zeitschrift, Vol. 289, No. 1-2: pp. 455-469
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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.