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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
DOI: https://doi.org/10.1090/S0002-9939-1994-1209101-9
MathSciNet review: 1209101
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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?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1209101-9
Keywords: Paradoxical decomposition, Baire category, Baire property
Article copyright: © Copyright 1994 American Mathematical Society