Some remarks concerning the attractors of iterated function systems (Q404489)

Let \(A\) be attractor of an iterated function system \(\{f_1, f_2, \dots, f_n \}\) and \(A_k =f_k(A)\) for \(k=1, 2, \dots, n.\) The authors show that under the assumptionsNEWLINENEWLINE(a) \(A_i \cap A_j\) is totally disconnected for every \(i\not=j\),NEWLINENEWLINE(b) \(A_i \cap A_j \cap A_k =\emptyset\) for any different numbers \(i, j, k\),NEWLINENEWLINE(c) all functions \(f_k\) are injective on \(A\)NEWLINENEWLINEthe set \(A\) is dendrite if and only if the graph of intersections of the sets \(A_k\), \(k=1, 2, \dots, n,\) is a tree.