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A continuous movement version of the Banach—Tarski paradox: A solution to de Groot's Problem

Wilson, Trevor M. (2005) A continuous movement version of the Banach—Tarski paradox: A solution to de Groot's Problem. Journal of Symbolic Logic, 70 (3). pp. 946-952. ISSN 0022-4812. http://resolver.caltech.edu/CaltechAUTHORS:WILjsl05

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Abstract

In 1924 Banach and Tarski demonstrated the existence of a paradoxical decomposition of the 3-ball B, i.e., a piecewise isometry from B onto two copies of B. This article answers a question of de Groot from 1958 by showing that there is a paradoxical decomposition of B in which the pieces move continuously while remaining disjoint to yield two copies of B. More generally, we show that if n ≥ 2, any two bounded sets in


Item Type:Article
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http://dx.doi.org/10.2178/jsl/1122038921DOIUNSPECIFIED
http://projecteuclid.org/euclid.jsl/1122038921PublisherUNSPECIFIED
Additional Information:2005 © Association for Symbolic Logic. Received January 20, 2005; accepted May 9, 2005. This paper is the result of an undergraduate research project supported by an NSF grant. The author would like to thank Prof. A.S. Kechris of Caltech for his time and guidance. Research supported by NSF Grant DMS 9987437.
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National Science FoundationDMS 9987437
Record Number:CaltechAUTHORS:WILjsl05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:WILjsl05
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Deposited On:09 Oct 2008 23:56
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