Thread: Lipschitz continuity

Let X and Y are Metric spaces and X is compact

f:X--> Y is locally Lipschitz continuous for every xo in X there exists a ball B(xo)

how to prove f is globally Lipschitz continuous for all x,y belongs X
st d(f(x),f(y))<=Ld(x,y)


Can anyone help with this problem.

Thank you

Suppose and let U_x be the Lipschitz n.hood of x, with Lipschitz constant L_x. What can you say about ? How can you pick the Lipschitz (global) constant?

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