A continuous version of the Hausdorff¨CBanach¨CTarski paradox

详细信息    查看全文

• 作者：V. A. Churkin
• 关键词：Hausdorff– ; Banach– ; Tarski paradox ; continuous decompositions ; free subgroups of rotation group of Euclidean space
• 刊名：Algebra and Logic
• 出版年：2010
• 出版时间：March, 2010
• 年：2010
• 卷：49
• 期：1
• 页码：91-98
• 全文大小：186.1 KB

文摘

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.