1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Closed set

  1. Apr 29, 2010 #1
    1. The problem statement, all variables and given/known data

    on the complex line, with the usual metric, I need to determine if this is a closed set.

    [tex] A = \left\{\left|\frac{1}{z^{2}+1} \right|: |z| = 1 ; z\neq \pm i\right \} [/tex]

    2. Relevant equations



    3. The attempt at a solution

    A closed set implies that the set of all limit points belongs to A.

    Usually I'm given a function, and I take an arbitrary convergent sequence and show whether or not that point to which it converges is in A or not. But when I have just a set like this, I'm unsure of how to do that. Any advice?
     
  2. jcsd
  3. Apr 29, 2010 #2
    Try finding a way to figure out what points are in the set.

    Also, you might find it worthwhile to think of A as the image (your prof might call it the range) of the function [itex]f\colon \{z:|z|=1, z\neq\pm i\}\to\mathbb{C}[/itex] defined by
    [tex] f(z) = \left|\frac{1}{z^2+1}\right|.[/tex]​
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Closed set
  1. Closed set? (Replies: 12)

  2. Closed set (Replies: 3)

  3. Closed sets (Replies: 8)

  4. Closed set (Replies: 11)

  5. Closed set (Replies: 14)

Loading...