Proving Space of Differential Functions Not Closed

[lady99]

how i prove that space of defrential function not closed?

 

[Fredrik]

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?

 

[lady99]

{x:xis polynomail} subset c[a,b]}

 

[mrbohn1]

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!

 

[HallsofIvy]

I would interpret "c[a, b]" as the set of functions continuous 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.