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Banach-Tarski paradox in some complete manifolds

Author: Grzegorz Tomkowicz
Journal: Proc. Amer. Math. Soc. 145 (2017), 5359-5362
MSC (2010): Primary 03E05, 20E05; Secondary 22E15, 05C63
Published electronically: August 29, 2017
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Abstract: We generalize the Banach-Tarski paradox showing that this theorem holds in the metric spaces in which bounded and closed sets are compact, relative to continuous and transitive actions of non-solvable Lie groups whose non-identity elements has small sets of fixed points (i.e., the points are irrelevant in the considered constructions).

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Additional Information

Grzegorz Tomkowicz
Affiliation: Centrum Edukacji $G^{2}$, ul. Moniuszki 9, 41-902 Bytom, Poland

Keywords: Banach--Hausdorff--Tarski paradox, complete manifolds, Laczkovich's criterion, Lie groups
Received by editor(s): July 16, 2016
Received by editor(s) in revised form: December 31, 2016
Published electronically: August 29, 2017
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2017 American Mathematical Society

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