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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-1992-1098399-4
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?)

  • [1] Mahlon M. Day, Normed linear spaces, 3rd ed., Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21. MR 0344849
  • [2] M. Edelstein, K. Johnson, and A. C. Thompson, On the isometric dissection problem for convex sets, Studia Sci. Math. Hungar. 27 (1992), no. 3-4, 273–277. MR 1218147
  • [3] Stan Wagon, The Banach-Tarski paradox, Encyclopedia of Mathematics and its Applications, vol. 24, Cambridge University Press, Cambridge, 1985. With a foreword by Jan Mycielski. MR 803509

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DOI: https://doi.org/10.1090/S0002-9939-1992-1098399-4
Article copyright: © Copyright 1992 American Mathematical Society