Results 1 to 4 of 4

Math Help - example of sequence of functions

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    1

    example of sequence of functions

    Can anyone think of an example of a sequence of functions f_n:[0,1]\to\mathbb{R} that converges uniformly on (0,1) but not on [0,1]?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    I assume the functions need to be continuous, in which case no such sequence exists. The behavior of a continuous function is determined by its behavior on any dense subset.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by retep View Post
    Can anyone think of an example of a sequence of functions f_n:[0,1]\to\mathbb{R} that converges uniformly on (0,1) but not on [0,1]?

    If we don't assume f_n need to be continuous a trivial example is:

    f_n(x)=\begin{Bmatrix} 0 & \mbox{ if }& x\in [0,1)\\(-1)^n & \mbox{if}& x=1\end{matrix}


    Fernando Revilla
    Last edited by FernandoRevilla; February 21st 2011 at 03:59 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2011
    Posts
    18
    can someone help me , i now what does mean the sequence of real number , but i confused what does it mean by sequence of vector space? for example vector space of polynomials ? and n*m matrices ?how would be their sentences of the related sequences? and why the convergent of these sequences depends on the norm that we define for these spaces ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sequence of functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 15th 2011, 06:47 PM
  2. Example of sequence of functions
    Posted in the Differential Geometry Forum
    Replies: 9
    Last Post: May 1st 2011, 12:11 PM
  3. Sequence of functions
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: April 3rd 2011, 05:37 PM
  4. Lim sup of a sequence of functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 24th 2009, 10:34 AM
  5. sequence of functions
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 14th 2008, 04:16 PM

Search Tags


/mathhelpforum @mathhelpforum