  We continue to study topological properties of the group Homeo(X) of all
homeomorphisms of a Cantor set X with respect to the uniform topology tau,
which was started in the paper (S. Bezuglyi, A.H. Dooley, and J. Kwiatkowski,
Topologies on the group of homeomorphisms of a Cantor set, ArXiv e-print
math.DS/0410507, 2004). We prove that the set of periodic homeomorphisms is
tau-dense in Homeo(X) and deduce from this result that the topological group
(Homeo(X), tau) has the Rokhlin property, i.e., there exists a homeomorphism
whose conjugate class is tau-dense in Homeo(X). We also show that for any
homeomorphism T the topological full group [[T]] is tau-dense in the full group
[T].
