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Closed sets in C

  1. Jan 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Show by example that an infinite union of closed sets in [itex]\mathbb{C}[/itex] need not be closed.

    3. The attempt at a solution

    In [itex]\mathbb{R}[/itex] I know that an infinite union of the closed sets [itex]A_{n}=[1/n,1-1/n][/itex] is open. Not sure if it works in [itex]\mathbb{C}[/itex] as well.
     
  2. jcsd
  3. Jan 24, 2012 #2

    SammyS

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    Try closed balls, or closed rectangles.
     
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