We continue the study of topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology τ, which was started by Bezuglyi, Dooley, Kwiatkowski and Medynets. We prove that the set of periodic homeomorphisms is τ-dense in Homeo(X) and deduce from this result that the topological group (Homeo(X),τ) has the Rokhlin property, i.e., there exists a homeomorphism whose conjugacy class is τ-dense in Homeo(X). We also show that for any homeomorphism T the topological full group [[T]] is τ-dense in the full group [T].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm194-1-1,
author = {Konstantin Medynets},
title = {On approximation of homeomorphisms of a Cantor set},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {1-13},
zbl = {1131.37014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm194-1-1}
}
Konstantin Medynets. On approximation of homeomorphisms of a Cantor set. Fundamenta Mathematicae, Tome 193 (2007) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm194-1-1/