Abstract
We give a simple procedure to convert a uniform homotopy F into a Lipschitz homotopy H for a large class of domain and target spaces. In this procedure, we use the modulus of continuity of F to estimate the Lipschitz constant of H. For Lipschitz homotopy in the time direction, our result is related to a theorem due to A. Calder and J. Siegel. As an application of our result, a Lipschitz version of a theorem of J. West is given.
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