Results 1 to 2 of 2

Math Help - Uniform metric in R^w

  1. #1
    Member ModusPonens's Avatar
    Joined
    Aug 2010
    Posts
    125
    Thanks
    14

    Uniform metric in R^w

    Hello

    I'm having trouble understanding something in Munkre's topology book. It's exercise 20.6.(a).

    It says: Let \rho be the uniform metric on R^{\omega}. Given x=(x_1,x_2,...) \in  R^{\omega} and given 0< \epsilon <1, let U(x, \epsilon )=(x_1- \epsilon,x_1 + \epsilon) \times ... \times (x_n- \epsilon , x_n+ \epsilon) \times ... .

    (a) Show that U(x, \epsilon ) is different from the \epsilon-ball B_{\rho}(x, \epsilon )

    Now, I found a solution to this exercise that said that the point (x_1+ (1/2) . \epsilon , x_2+ (2/3) . \epsilon , x_3 + (3/4) . \epsilon , ...) belonged to U, but not to the ball. How so?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member ModusPonens's Avatar
    Joined
    Aug 2010
    Posts
    125
    Thanks
    14

    Re: Uniform metric in R^w

    Ok, with help on another forum, I understood what was going on.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 8th 2011, 03:16 PM
  2. Replies: 1
    Last Post: October 31st 2010, 08:09 PM
  3. uniform differentiable => uniform continuity
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: November 30th 2009, 04:19 PM
  4. standard metric and discrete metric
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 24th 2009, 08:25 AM
  5. Uniform Continuous and Uniform Convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 28th 2007, 03:51 PM

Search Tags


/mathhelpforum @mathhelpforum