1. The problem statement, all variables and given/known data a) Let V be a normed vector space. Then show that (by the triangle inequality) the function f(x)=||x|| is a Lipschitz function from V into [0,∞). In particular, f is uniformly continuous on V. b) Show that a closed subset F of contains an element of minimal norm, that is, there is an x E F such that ||x||≤||y|| for all y E F. (here ||x|| refers to the usual Euclidean norm). (hint: F may not be compact, so work on a suitable compact subset of F.) 2. Relevant equations 3. The attempt at a solution I proved part a, but I really have no idea how to do part b. Why do we need compactness, and what is the suitable compact subset of F? I hope someone can help me out! Thank you!