How do you show that the closure of [a,b] is not closed in C0[a,b]?
C0[a,b] is .. the space of continuous functions with compact support..?
If the answer is affirmative then i cant help you, [a,b] is not a subset of C0[a,b] .
If the answer is negative then i cant help you since i dont know what you mean with C0[a,b].
Need context
Assuming I follow you, consider the set of functions on [0,1]:
fn(x) = $\displaystyle x^{(p+n)} \forall n=1,2,3...$
These functions are clearly p times differentiable. But, as n goes to infinity, the functions converge to the function f(x) where
f(x) = 0 if $\displaystyle x\not=$ 1 and f(x) = 1 if x=1, which is not continuous
I think what southprkfan1 thought vinnie100 meant was:What did you think he meant? I don't actually understand what he was asking for.
Prove that $\displaystyle \mathcal C^p([a,b])$ is not closed on $\displaystyle \mathcal C([a,b])$
where $\displaystyle C^p([a,b])$ is the set of functions with p continuous derivative on [a,b] and $\displaystyle \mathcal C([a,b])$ the set of continuous functions