Closed space

  • Thread starter lady99
  • Start date
  • #1
lady99
4
0
how i prove that space of defrential function not closed?
 

Answers and Replies

  • #2
Fredrik
Staff Emeritus
Science Advisor
Gold Member
10,872
420
You need to give us more details. Closed in the sense of topology or closed in the sense of being a subspace of a vector space (or a group or whatever)? Do you mean differential? What sort of objects is it acting on? Just real-valued functions of one real variable?
 
  • #3
lady99
4
0
{x:xis polynomail} subset c[a,b]}
 
  • #4
mrbohn1
97
0
Still not enough information! If I were to guess, then it would be that you want to know how to prove that the space of differentiable functions between 2 topological spaces is not closed under some topology.

Is this correct? If so, which topology? Don't hold back!
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
43,010
969
I would interpret "c[a, b]" as the set of functions continous on [a, b] but the orignal post said "differentiable" which would be "c1[a, b]".

So I take it you want to show that the set of all polynomials is not closed as a subset of the set of all differentiable functions on some interval.

But it is still not clear if you mean "closed" under some operation or "closed" in some topology. And, we would need to know what operation or topology is involved.
 

Suggested for: Closed space

  • Last Post
Replies
6
Views
14K
  • Last Post
Replies
2
Views
813
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
4
Views
6K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
7
Views
13K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
7
Views
8K
  • Last Post
Replies
12
Views
4K
Top