Homeomorphism groups of Sierpinski carpets and Erdos space

Eras space E is the "rational" Hilbert space, that is, the set of vectors in l(2) with all coordinates rational. Eras proved that E is one-dimensional and homeomorphic to its own square x which makes it an important example in dimension theory. Dijkstra and van Mill found topological characterizations of Let M(n)(n+1), n is an element of N, be the n-dimensional Menger continuum in R(n+1), also known as the n-dimensional Sierpinski carpet, and let D be a countable dense subset of M(n)(n+ 1). We consider the topological group H(M(n)(n+1), D) of all autohomeomorphisms of M(n)(n+1) that map D onto itself, equipped with the compact-open topology. We show that under some conditions on D the space H(M(n)(n+1), D) is homeomorphic to E for n is an element of N \ {3}.