1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Closed space

  1. Mar 14, 2010 #1
    how i prove that space of defrential function not closed?
  2. jcsd
  3. Mar 14, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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?
  4. Mar 15, 2010 #3
    {x:xis polynomail} subset c[a,b]}
  5. Mar 15, 2010 #4
    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!
  6. Mar 16, 2010 #5


    User Avatar
    Science Advisor

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook