On approximation of homeomorphisms of a Cantor set

• Autorzy: Konstantin Medynets
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 54H11: Topological groups
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 194
• Numer: 1
• Strony: 1-13

Daty

wydano

2007

Twórcy

autor

Konstantin Medynets

• Department of Mathematics, Institute for Low Temperature Physics, 47 Lenin ave., 61103 Kharkov, Ukraine

Identyfikatory

DOI

10.4064/fm194-1-1