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I Can someone explain these two examples of an open set

  1. Oct 23, 2016 #1
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  3. Oct 23, 2016 #2


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    4) Apparently they have already proven that the open ball in R is an open set. That may be their original definition of an open set. They have also proven that any union of open sets is open. So all they need to do is to rewrite the original set of 4) as the union of balls.
    5) Same logic as in 4) except that the balls are in the complex plane, C.
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