A Vitali set can be homeomorphic to its complement

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• 作者：A. Nowik
• 关键词：Vitali set ; Bernstein set ; Hamel base ; paradoxical decompositions
• 刊名：Acta Mathematica Hungarica
• 出版年：2007
• 出版时间：April, 2007
• 年：2007
• 卷：115
• 期：1-2
• 页码：145-154
• 全文大小：304 KB

文摘

We prove that there exists a special homeomorphism of the Cantor space such that every noncancellable composition of finite powers and translations of rational numbers has no fixed point. For this homeomorphism there exists both a Vitali and Bernstein subset of the Cantor set such that the image of this set is equal to its complement. There exists a Bernstein and Vitali set such that there is no Borel isomorphism between this set and its complement.