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On the indecomposability of compact convex sets

Author: Michael Edelstein
Journal: Proc. Amer. Math. Soc. 115 (1992), 737-739
MSC: Primary 52A07
MathSciNet review: 1098399
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Abstract: Let $ C$ be a compact convex set in a Hausdorff, locally convex linear topological space $ X$ and let $ \mathcal{F}$ be the family of affine homeomorphisms of $ X$ onto itself. It is proved that $ C$ is indecomposable under $ \mathcal{F}$; i.e. if $ C = A \cup B$ and $ B = F[A]$, for some $ F \in \mathcal{F}$, then $ A \cap B \ne \emptyset $.

References [Enhancements On Off] (What's this?)

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