Answer to Question #211546 in Real Analysis for Matome

Question

Let k ≥ 0 and f : M → M a k-Lipschitz function. Let ε > 0. Give the largest

number φ > 0, if any, such that ∀x, y ∈ M, d(x, y) < φ implies d(f(x), d(y)) < ε.