A mapping \(f:{X\rightarrow X}\) , where X is a compact metric space, is strongly mixing if for each nonempty open subset U of X and for each \(x\in X\) , there exists \(N\in \mathbb {N}\) such that if \(n\geqslant N\) , then \(x\in f^n(U)\) , and f is exact if for each nonempty open subset U of X there exists \(n\in \mathbb {N}\) such that \(f^n(U)=X\) . It is easy to prove that if X is a tree and f is a strongly mixing mapping, then f is exact. We show that this result cannot be extended to dendrites, by proving that for each dendrite D which is not a tree, there exists a continuous function \(f:D\rightarrow D\) that is strongly mixing but it is not exact.
