The space of adding machines generated by continuous self maps of manifolds

Let M be the Cantor space or an n-dimensional manifold with C ( M , M ) the set of continuous self-maps of M, and S α ( M ) = { ( x , f ) ∈ M × C ( M , M ) : ω ( x , f ) is an α - adic adding machine } . We prove the following:(1) ∞ , then S α ( M ) is a nowhere dense subset of M × C ( M , M ) that contains no isolated points. β , then S α ( M ) ⊆ S β ( M ) ¯ .