  Let $M$ be a compact Riemannian manifold. The set $\text{F}^{r}(M)$
consisting of sequences $(f_{i})_{i\in\mathbb{Z}}$ of $C^{r}$-diffeomorphisms
on $M$ can be endowed with the compact topology or with the strong topology. A
notion of topological entropy is given for these sequences. I will prove this
entropy is discontinuous at each sequence if we consider the compact topology
on $\text{F}^{r}(M)$. On the other hand, if $ r\geq 1$ and we consider the
strong topology on $\text{F}^{r}(M)$, this entropy is a continuous map.
