A note on a property of a weak self-similar perfect set

Let S be a compact, weak self-similar perfect set based on a system of weak contractions f(j), j = 1,..., m each of which is characterized by a variable contraction coefficient alpha(j)(l) as d(f(j)(x)f(j)(y)) less than or equal to alpha(j)(l)d(x,y), d(x,y) < l,l > 0. If the relation Sigma(j=1)(m) alpha(j)(l(o)) < 1 holds at at least one point l(0), then every nonempty compact metric space is a continuous image of the set S. (C) 2002 Elsevier Science Ltd. All rights reserved.