On a dendrite generated by a zero-dimensional weak self-similar set

Let S be a zero-dimensional, perfect, compact weak self-similar set generated in dendrite X by a family {f_j} of weak contractions from X to itself. Decomposition space D_f of S due to a continuous mapping f from S onto X is also a dendrite. In the dendrite D_f, there exists a zero-dimensional, perfect, compact weak self-similar set S¹ based on a family {f_j¹} each of which is topologically conjugate to f_j. Decomposition space D_f¹ of S¹ due to a continuous mapping f¹ from S¹ onto D_f is again a dendrite. In this manner, through the successive formation of weak self-similar set, we can obtain a sequence X, D_f, D_f¹, ... of dendrite any pair in which are mutually homeomorphic.