On a decomposition space of a weak self-similar set

Under some conditions concerning the weak contractions fj (d(fj(x), fj(y)) αj(l)d(x, y) for d(x, y) < l, l > 0, 0 < αj(l) < 1), j = 1, … , m defined on a compact metric space X, a decomposition space of the weak self-similar set generated by the system fj, j = 1, … , m is proved to be homeomorphic to X.