On a topological embedding of a weak self-similar, zero-dimensional set

If a compact, weak self-similar set is generated from a system of weak contractions fj, j=1,…,m whose variable contraction coefficients αj(l), j=1,…,m are characterized by the relation that ∑j=1mαj(l0)<1 for some l0>0, then the weak self-similar set can be topologically embedded in a topological space which has the property that every nonempty compact metric space is a continuous image of it.