Banach-Tarski paradox in some complete manifolds

Tomkowicz, Grzegorz

doi:10.1090/proc/13657

Banach-Tarski paradox in some complete manifolds
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Proc. Amer. Math. Soc. 145 (2017), 5359-5362 Request permission

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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