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Algebra i logika, 2010, Volume 49, Number 1, Pages 135–145 (Mi al431)  

This article is cited in 3 scientific papers (total in 3 papers)

A continuous version of the Hausdorff–Banach–Tarski paradox

V. A. Churkinab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (163 kB) Citations (3)
References:
Abstract: We come up with a simple proof for a continuous version of the Hausdorff–Banach–Tarski paradox, which does not make use of Robinson's method of compatible congruences and fits in the case of finite and countable paradoxical decompositions. It is proved that there exists a free subgroup whose rank is of the power of the continuum in a rotation group of a three-dimensional Euclidean space. We also argue that unbounded subsets of Euclidean space containing inner points are denumerably equipollent.
Keywords: Hausdorff–Banach–Tarski paradox, continuous decompositions, free subgroups of rotation group of Euclidean space.
Received: 01.12.2008
English version:
Algebra and Logic, 2010, Volume 49, Issue 1, Pages 91–98
DOI: https://doi.org/10.1007/s10469-010-9080-y
Bibliographic databases:
Document Type: Article
UDC: 512.543.12
Language: Russian
Citation: V. A. Churkin, “A continuous version of the Hausdorff–Banach–Tarski paradox”, Algebra Logika, 49:1 (2010), 135–145; Algebra and Logic, 49:1 (2010), 91–98
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/al/v49/i1/p135
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
     
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