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 fj, j=1,…,m each of which is characterized by a variable contraction coefficient αj(l) as d(fj(x),fj(y)) αj(l)d(x,y), d(x,y)0. If the relation ∑mj=1αj(l0)<1 holds at at least one point l0, then every nonempty compact metric space is a continuous image of the set S.