We prove that if a mixing map f: [0, 1]⟶[0, 1] belongs to the C0-closure of the set of iterates and f(0) ≠ 0, f(1) ≠ 1 then f is an iterate itself. Together with some one-dimensional techniques it implies that the set of all iterates is nowhere dense in C([0, 1], [0, 1]) giving the final answer to the question of A. Bruckner, P. Humke and M. Laczkovich. © 1992 by American Mathematical Society.
