  Let f be a chain mixing continuous onto mapping from the Cantor set onto
itself. Let g be a homeomorphism on the Cantor set that is topologically
conjugate to a subshift. Then, homeomorphisms that are topologically conjugate
to g approximate f in the topology of uniform convergence if a trivial
necessary condition on the periodic points holds. In particular, if f is a
chain mixing continuous onto mapping from the Cantor set onto itself with a
fixed point, then homeomorphisms on the Cantor set that are topologically
conjugate to a subshift approximate f in the topology of uniform convergence.
In addition, homeomorphisms on the Cantor set that are topologically conjugate
to a subshift without periodic points approximate any chain mixing continuous
onto mappings from the Cantor set onto itself. In particular, let f be a
homeomorphism on the Cantor set that is topologically conjugate to a full
shift. Let g be a homeomorphism on the Cantor set that is topologically
conjugate to a subshift. Then, a sequence of homeomorphisms that is
topologically conjugate to g approximates f.
