Results 1 to 1 of 1

Math Help - Counterexample to uniformly convergence

  1. #1
    Newbie
    Joined
    Feb 2009
    From
    Valparaíso, Chile
    Posts
    9

    Counterexample to uniformly convergence

    Hi! My problem is this: Find an example of (f_n), a sequence of functions on \mathcal{C}(X,\mathbb{R}) (continuous with domain X and real-valued) such that: X is NOT compact, (f_n) be equicontinuous and pointwise bounded, and every subsequence uniformly convergent have the same limit (call him f. In fact, may there's no subsequence uniformly convergent, and we aren't saying that every subsequence is uniformly convergent). I need to find a sequence that satisfy this conditions and NOT converges to f uniformly.

    Thanks

    Edit: I think that I don't need your help now =) With f_n(x)=\dfrac{x}{n},\;X=\mathbb{R} holds
    Last edited by Pedro²; December 4th 2009 at 01:37 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Counterexample
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 26th 2010, 10:17 AM
  2. uniformly convergence
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: December 31st 2009, 12:16 AM
  3. Counterexample for convergence in L1
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 24th 2009, 12:04 PM
  4. counterexample of convergence of integral again
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: May 1st 2009, 07:36 PM
  5. A counterexample
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: November 1st 2006, 10:06 AM

Search Tags


/mathhelpforum @mathhelpforum