Geodesic
A continuous version of the Hausdorff–Banach–Tarski paradox
Algebra i logika, Tome 49 (2010) no. 1, pp. 135-145

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Mots-clés : Hausdorff–Banach–Tarski paradox
Keywords: continuous decompositions, free subgroups of rotation group of Euclidean space. 
@article{AL_2010_49_1_a5,
     author = {V. A. Churkin},
     title = {A continuous version of the {Hausdorff{\textendash}Banach{\textendash}Tarski} paradox},
     journal = {Algebra i logika},
     pages = {135--145},
     publisher = {mathdoc},
     volume = {49},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2010_49_1_a5/}
}
TY  - JOUR
AU  - V. A. Churkin
TI  - A continuous version of the Hausdorff–Banach–Tarski paradox
JO  - Algebra i logika
PY  - 2010
SP  - 135
EP  - 145
VL  - 49
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2010_49_1_a5/
LA  - ru
ID  - AL_2010_49_1_a5
ER  - 
%0 Journal Article
%A V. A. Churkin
%T A continuous version of the Hausdorff–Banach–Tarski paradox
%J Algebra i logika
%D 2010
%P 135-145
%V 49
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2010_49_1_a5/
%G ru
%F AL_2010_49_1_a5
V. A. Churkin. A continuous version of the Hausdorff–Banach–Tarski paradox. Algebra i logika, Tome 49 (2010) no. 1, pp. 135-145. http://geodesic.mathdoc.fr/item/AL_2010_49_1_a5/