I am havig some trouble with topology. If you have a metric space which is totally bounded en locally compact, is it then compact? At first I though that this was not true. I tried some dicrete metric space and it failed. I tried to take the space of rational numbers with the interval [0,1] and it failed. So I could not find a good couterexample. I also could not prove that it is true... I still believe there is a counterexample. Any tips?