出版者:Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
ISSN:1588-2632
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.