Connectedness of the set of central Lyapunov exponents

In this brief note we prove that there is a residual subset $\mathcal{R}$ of $\textrm{Diff}^1(M)$ such that for any $f\in\mathcal{R}$ and any partially hyperbolic homoclinic class $H(p,f)$ with one dimensional center direction, the set of central Lyapunov exponents associated to the ergodic with full support is an interval. Also, some remarks on the general case presented.