Let $A=C[0,1]$ and $B=\{f\in A|f(0)=0\}$. What is the closure of B w.r.t the $|| . ||_\infty$ norm.
I really have a very poor intuitive grasp of this problem and I'm not sure where to begin?
I know $|| f ||_\infty=\sup_{x\in[0,1]} f(x)$ and that the closure is the limit points of B
Thansk for any help