Results 1 to 2 of 2

Math Help - Uniform Continuity Proof

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    60

    Uniform Continuity Proof

    Hi,
    I'm not sure how to prove this statement:

    Suppose f is uniformly continuous on the set S and let T be the image of S under f. Also assume that the function g is uniformly continuous on T. Prove that g o f is uniformly continuous on S?

    Thanks a lot!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by AKTilted View Post
    Hi,
    I'm not sure how to prove this statement:

    Suppose f is uniformly continuous on the set S and let T be the image of S under f. Also assume that the function g is uniformly continuous on T. Prove that g o f is uniformly continuous on S?

    Thanks a lot!
    So, you're trying to show that given \varepsilon>0 there exists \delta>0 such that for all x,y\in S |x-y|<\delta\implies |f(g(x))-f(g(y))|<\varepsilon, right?

    Ok, so what's the first step? You're lcearly going to want to consider two deltas one for the S and one for T. Which should you pick first?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Grade My Uniform Continuity Proof
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: November 8th 2010, 08:13 AM
  2. uniform continuity proof
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 27th 2009, 05:36 PM
  3. Uniform Continuity Proof
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 18th 2007, 05:23 PM
  4. Uniform Continuity Proof 2
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 16th 2007, 05:28 PM
  5. Uniform Continuity Proof
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 15th 2007, 03:42 AM

Search Tags


/mathhelpforum @mathhelpforum