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 f(j), j = 1,...,m whose variable contraction coefficients alpha(j)(l), j = 1,...,m are characterized by the relation that Sigma(j=1)(m) alpha(j)(l(0)) < 1 for some l(0) > 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. (C) 2004 Elsevier Ltd. All rights reserved.