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Openness of subsets of the integers.

  1. Oct 28, 2011 #1
    1. What are all the open subsets of the subspace Z of R.



    2. Relevant equations: def of openness



    3. I think the solution is all the subsets of Z, but I can't see how, for example you can say the subset of Z: {1} has a B(1,r) with r>0 is contained in {1}.

    Thanks for any help.
     
  2. jcsd
  3. Oct 28, 2011 #2

    HallsofIvy

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    You don't. It is easy to show that every singleton set is closed. But only finite intersections of closed sets are closed so only complements of finite sets are open.
     
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