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For an amenable minimal topologically free dynamical system $\alpha$ of agroup on a compact metrizable space $Z$ and for a compact metrizable space $Y$satisfying a mild condition, we construct a minimal skew product extension of$\alpha$ on $Z\times Y$. This generalizes a result of Glasner and Weiss. Wealso study the pure infiniteness of the crossed products of minimal dynamicalsystems arising from this result. In particular, we give a generalization of aresult of R{\o}rdam and Sierakowski.

Construction of minimal skew products of amenable minimal dynamical systems