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We consider continuous $SL(2,\mathbb{R})$-cocycles over a strictly ergodichomeomorphism which fibers over an almost periodic dynamical system(generalized skew-shifts). We prove that any cocycle which is not uniformlyhyperbolic can be approximated by one which is conjugate to an$SO(2,\mathbb{R})$-cocycle. Using this, we show that if a cocycle's homotopyclass does not display a certain obstruction to uniform hyperbolicity, then itcan be $C^0$-perturbed to become uniformly hyperbolic. For cocycles arisingfrom Schr\"odinger operators, the obstruction vanishes and we conclude thatuniform hyperbolicity is dense, which implies that for a generic continuouspotential, the spectrum of the corresponding Schr\"odinger operator is a Cantorset.

Cantor Spectrum for Schr\"odinger Operators with Potentials arising from Generalized Skew-shifts