On the indecomposability of compact convex sets
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- by Michael Edelstein PDF
- Proc. Amer. Math. Soc. 115 (1992), 737-739 Request permission
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
- Mahlon M. Day, Normed linear spaces, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21, Springer-Verlag, New York-Heidelberg, 1973. MR 0344849
- 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
- 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, DOI 10.1017/CBO9780511609596
Additional Information
- © Copyright 1992 American Mathematical Society
- 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