  We study the spectral types of the families of discrete one-dimensional
Schr\"odinger operators $\{H_\omega\}_{\omega\in\Omega}$, where the potential
of each $H_\omega$ is given by $V_\omega(n)=f(T^n\omega)$ for $n\in\mathbb{Z}$,
$T$ is an ergodic homeomorphism on a compact space $\Omega$ and
$f:\Omega\rightarrow\mathbb{R}$ is a continuous function. We show that a
generic operator $H_\omega\in \{H_\omega\}_{\omega\in\Omega}$ has purely
continuous spectrum if $\{T^n\alpha\}_{n\geq0}$ is dense in $\Omega$ for a
certain $\alpha\in\Omega$. We also show the former result assuming only that
$\{\Omega, T\}$ satisfies topological repetition property ($TRP$), a concept
introduced by Boshernitzan and Damanik (arXiv:0708.1263v1). Theorems presented
in this paper weaken the hypotheses of the cited research and allow us to reach
the same conclusion as those authors. We also provide a proof of Gordon's
lemma, which is the main tool used in this work.
