Generically there is but one self homeomorphism of the cantor set

Ethan Akin*, Eli Glasner, Benjamin Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

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.

Original languageEnglish
Pages (from-to)3613-3630
Number of pages18
JournalTransactions of the American Mathematical Society
Volume360
Issue number7
DOIs
StatePublished - Jul 2008

Keywords

  • Conjugacy class
  • Group of homeomorphisms of the cantor set
  • Rohlin property

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