
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 $\displaystyle x \in X$ and let U_x be the Lipschitz n.hood of x, with Lipschitz constant L_x. What can you say about $\displaystyle \bigcup_{x\in X}U_x$? How can you pick the Lipschitz (global) constant?
