Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Baire paradoxical decompositions need at least six pieces

Author: Friedrich Wehrung
Journal: Proc. Amer. Math. Soc. 121 (1994), 643-644
MSC: Primary 54E52; Secondary 04A20, 54E45, 54G15
MathSciNet review: 1209101
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that in certain cases paradoxical decompositions of compact metric spaces using sets (or even [0, 1 ]-valued functions) with the property of Baire modulo meager sets need more pieces than paradoxical decompositions with unrestricted pieces. In particular, any Baire paradoxical decomposition of the sphere $ {S^2}$ using isometries needs at least six pieces.

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

  • [1] Randall Dougherty and Matthew Foreman, Banach-Tarski paradox using pieces with the property of Baire, Proc. Nat. Acad. Sci. U.S.A. 89 (1992), no. 22, 10726–10728. MR 1190902,
  • [2] John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. MR 584443
  • [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
  • [4] Friedrich Wehrung, Théorème de Hahn-Banach et paradoxes continus ou discrets, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 6, 303–306 (French, with English summary). MR 1046500

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54E52, 04A20, 54E45, 54G15

Retrieve articles in all journals with MSC: 54E52, 04A20, 54E45, 54G15

Additional Information

Keywords: Paradoxical decomposition, Baire category, Baire property
Article copyright: © Copyright 1994 American Mathematical Society