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One knows that the set of quasi-periodic Schr\"odinger cocycles with positiveLyapunov exponent is open and dense in the analytic topology. In this paper, weconstruct cocycles with positive Lyapunov exponent which can be approximated byones with zero Lyapunov exponent in the space of ${\cal C}^ l$ ($1 \le l\le\infty$) smooth quasi-periodic cocycles. As a consequence, the set ofquasi-periodic Schr\"odinger cocycles with positive Lyapunov exponent is not${\cal C}^ l$ open.

Quasi-Periodic Schr\"odinger Cocycles with Positive Lyapunov Exponent are not Open in the Smooth Topology