Results 1 to 5 of 5

Math Help - Proving Continuity

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    17

    Proving Continuity

    I have the function (a,b),U_{(a,b)})\rightarrow((c,d),U_{(c,d)})" alt="f(a,b),U_{(a,b)})\rightarrow((c,d),U_{(c,d)})" />, where U_{(a,b)} is the subspace topology of the usual topology where A = (a,b) and U_{(c,d)} is the subspace topology of the usual topology where A = (c,d), defined as f(x)=\frac{d-c}{b-a}x+c-\frac{a(d-c)}{b-a}


    How do I show this function is continuous?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    It's a polynomial.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2010
    Posts
    17
    Quote Originally Posted by Tinyboss View Post
    It's a polynomial.
    I know all polynomials are continuous everywhere, but I have to actually show it is continuous, I can't just say it is continuous because it is a polynomial.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    Why are polynomials continuous? It comes down to sum and product behavior of limits. Of course, this polynomial is actually linear, so you can probably hammer out an epsilon-delta just for this one case if you prefer.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2010
    Posts
    17
    Quote Originally Posted by Tinyboss View Post
    Why are polynomials continuous? It comes down to sum and product behavior of limits. Of course, this polynomial is actually linear, so you can probably hammer out an epsilon-delta just for this case if you prefer.
    So for some (y_{1},y_{2}) in U_{(c,d)}, as y_{1}\rightarrow c^{+} and y_{2}\rightarrow d^{-}, f^{-1}((y_{1},y_{2}))\rightarrow (a,b), thus f^{-1}((y_{1},y_{2})) is in U_{(a,b)}.

    Would something like that work/be accurate?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving continuity
    Posted in the Differential Geometry Forum
    Replies: 12
    Last Post: May 15th 2011, 11:48 AM
  2. Proving Continuity
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 20th 2011, 10:49 PM
  3. proving continuity
    Posted in the Differential Geometry Forum
    Replies: 16
    Last Post: December 3rd 2010, 05:09 PM
  4. proving continuity of g(x, y) = x
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: November 18th 2009, 05:17 PM
  5. Proving Continuity
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 19th 2008, 04:27 AM

Search Tags


/mathhelpforum @mathhelpforum