Hey, I have a topology problem here:
Let K be a compact subset in R and let f : K → R be a continuous function. Prove
that for every ε > 0 there exists Lε > 0 such that
|f (x) − f (y)| ≤ Lε |x − y| + ε , for every x, y ∈ K.
I'm thinking of using the Lipschitz condition, but not quite sure how to handle it. Could you anyone please give me a hint? Any input is appreciated!