How do you show that the closure of [a,b] is not closed in C0[a,b]?
Printable View
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
Sorry I got it all wrong!
Its meant to say:
Show that a p times continuously differentiable function is not closed in a 0 times continuous differentiable function.
Assuming I follow you, consider the set of functions on [0,1]:Quote:
Originally Posted by vinnie100
fn(x) =
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 if1 and f(x) = 1 if x=1, which is not continuous
What did you think he meant? I don't actually understand what he was asking for.Quote:
Originally Posted by southprkfan1Assuming I follow you, consider the set of functions on [0,1]:
fn(x) =
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
I think what southprkfan1 thought vinnie100 meant was:Quote:
What did you think he meant? I don't actually understand what he was asking for.
Prove thatis not closed on
whereis the set of functions with p continuous derivative on [a,b] and
the set of continuous functions