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Math Help - Lipschitz continuity

  1. #1
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    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
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  2. #2
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    Suppose  x \in X and let U_x be the Lipschitz n.hood of x, with Lipschitz constant L_x. What can you say about \bigcup_{x\in X}U_x? How can you pick the Lipschitz (global) constant?
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  3. #3
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    ..
    Last edited by mathmad; November 25th 2009 at 08:20 AM. Reason: .
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