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Homework Help: Set of integers

  1. Oct 12, 2008 #1
    1. The problem statement, all variables and given/known data


    is the set of integers open or closed
    2. Relevant equations



    3. The attempt at a solution

    I thought not closed
    open because R/Z=Union of open intervals
    like ....U(-1,0)U(0,1)U.....
     
  2. jcsd
  3. Oct 12, 2008 #2

    morphism

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    You got it backwards!
     
  4. Oct 12, 2008 #3

    HallsofIvy

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    With what topology? The topology inherited from the reals? (That is, the metric topology with d(m,n)= |m- n|.)

    Morphism's point is that since R\Z is a union of a union of open intervals, The complement of Z is open and so Z itself is ?

    However, don't think that "open" or "closed" are all the options. It is possible for a set to be neither open nor closed. It is even possible for a set to be both open and closed.
     
  5. Oct 13, 2008 #4
    ow sorry I switched open and closed
    I meant that it was a closed set and not open
     
  6. Oct 13, 2008 #5

    morphism

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    Yes, then that's right. The set is closed and not open.
     
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