Banach-Tarski paradox in some complete manifolds
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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).References
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Additional Information
- Grzegorz Tomkowicz
- Affiliation: Centrum Edukacji $G^2$, ul. Moniuszki 9, 41-902 Bytom, Poland
- MR Author ID: 962797
- Email: gtomko@vp.pl
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5359-5362
- MSC (2010): Primary 03E05, 20E05; Secondary 22E15, 05C63
- DOI: https://doi.org/10.1090/proc/13657
- MathSciNet review: 3717962