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Cos(x) is not closed function?

  1. Mar 29, 2010 #1
    I think cos(x) is closed function in R.
    But I heard that cos(x) is not closed function in R.
    What do I choose closed set A in R, cos(A) is not closed in R?
    Help....
     
  2. jcsd
  3. Mar 29, 2010 #2

    quasar987

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    Consider for instance the set [itex]A := \{2n\pi-1/n: n\in\mathbb{N}\}[/itex]. It is closed, but cos(A) does not contain its limit point 1.
     
  4. Mar 29, 2010 #3
    Thank you, friend. I tried closed intervals...
     
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