Results 1 to 6 of 6

Math Help - closure

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    36

    closure

    How do you show that the closure of [a,b] is not closed in C0[a,b]?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member mabruka's Avatar
    Joined
    Jan 2010
    From
    Mexico City
    Posts
    150
    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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2010
    Posts
    36
    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.
    Last edited by vinnie100; March 26th 2010 at 08:36 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Feb 2010
    Posts
    147
    Quote Originally Posted by vinnie100 View Post
    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]:

    fn(x) = 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 x\not= 1 and f(x) = 1 if x=1, which is not continuous
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by southprkfan1 View Post
    Assuming I follow you, consider the set of functions on [0,1]:

    fn(x) = 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 x\not= 1 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.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member mabruka's Avatar
    Joined
    Jan 2010
    From
    Mexico City
    Posts
    150
    What did you think he meant? I don't actually understand what he was asking for.
    I think what southprkfan1 thought vinnie100 meant was:


    Prove that \mathcal C^p([a,b]) is not closed on \mathcal C([a,b])

    where C^p([a,b]) is the set of functions with p continuous derivative on [a,b] and \mathcal C([a,b]) the set of continuous functions
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Relation between topological closure and algebraic closure
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: November 4th 2010, 02:45 PM
  2. Closure
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 19th 2009, 01:59 AM
  3. closure
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 27th 2009, 01:03 PM
  4. Replies: 6
    Last Post: February 11th 2009, 12:56 PM
  5. Closure
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 6th 2009, 09:06 PM

Search Tags


/mathhelpforum @mathhelpforum