On approximation of homeomorphisms of a Cantor set

Konstantin Medynets. "On approximation of homeomorphisms of a Cantor set." Fundamenta Mathematicae 194.1 (2007): 1-13. <http://eudml.org/doc/283269>.

@article{KonstantinMedynets2007,
abstract = {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].},
author = {Konstantin Medynets},
journal = {Fundamenta Mathematicae},
keywords = {Borel automorphisms of a Cantor set; homeomorphism of a Cantor set; Rokhlin lemma; full group of a homeomorphism},
language = {eng},
number = {1},
pages = {1-13},
title = {On approximation of homeomorphisms of a Cantor set},
url = {http://eudml.org/doc/283269},
volume = {194},
year = {2007},
}

TY - JOUR
AU - Konstantin Medynets
TI - On approximation of homeomorphisms of a Cantor set
JO - Fundamenta Mathematicae
PY - 2007
VL - 194
IS - 1
SP - 1
EP - 13
AB - 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].
LA - eng
KW - Borel automorphisms of a Cantor set; homeomorphism of a Cantor set; Rokhlin lemma; full group of a homeomorphism
UR - http://eudml.org/doc/283269
ER -