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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Hahn–Banach theorem and a six-piece paradoxical decomposition of a ball
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by Haruka Sato and Masahiro Shioya PDF
Proc. Amer. Math. Soc. 150 (2022), 365-369 Request permission

Abstract:

The Banach–Tarski paradox holds using six pieces in Zermelo–Fraenkel set theory with the Hahn–Banach theorem.
References
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Additional Information
  • Haruka Sato
  • Email: harupie_529@yahoo.co.jp
  • Masahiro Shioya
  • Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan
  • MR Author ID: 336423
  • Email: shioya@math.tsukuba.ac.jp
  • Received by editor(s): September 14, 2020
  • Received by editor(s) in revised form: December 30, 2020
  • Published electronically: October 25, 2021
  • Communicated by: Heike Mildenberger
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 150 (2022), 365-369
  • MSC (2020): Primary 03E25, 46A22
  • DOI: https://doi.org/10.1090/proc/15550
  • MathSciNet review: 4335883