(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Closed set

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