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Homework Help: 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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    Science Advisor

    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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