Let . Is uniformly convergent on the interval [0,1]?
I don't think that it is uniformly convergent but I'm having a hard time proving it. I thought to use the theorem that it will be uniformly convergent iff , but I can't see how to show this. Any help?
Moreover, it might be feasible to prove that no subsequence of has a pointwise convergent subsequence on . The proof for why it cannot possess a pointwise convergent subequence on is easy...I'll see if I can adapt my proof.