Abstract
We describe a self-homeomorphism R of the Cantor set X and then show that its conjugacy class in the Polish group H(X) of all homeomorphisms of X forms a dense Gδ subset of H(X). We also provide an example of a locally compact, second countable topological group which has a dense conjugacy class. © 2008 American Mathematical Society.
Recommended Citation
E. Akin et al., "Generically There is But One Self Homeomorphism of the Cantor Set," Transactions of the American Mathematical Society, vol. 360, no. 7, pp. 3613 - 3630, American Mathematical Society, Jul 2008.
The definitive version is available at https://doi.org/10.1090/S0002-9947-08-04450-4
Department(s)
Mathematics and Statistics
Keywords and Phrases
Conjugacy class; Group of homeomorphisms of the cantor set; Rohlin property
International Standard Serial Number (ISSN)
0002-9947
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 American Mathematical Society, All rights reserved.
Publication Date
01 Jul 2008
