For the space of all continuous functions we can have the sup norm:
$|f|=\sup|f|$
I have also seen the following norm: $|f|=\sup|f(x)|/|x|$
I don't know what this norm is called and therefore can't find any information on it. What is the distinction?
what is this norm called? is the space $C[0,1]$ with this norm still complete?