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Open sets in R^2

  1. Apr 24, 2008 #1
    [SOLVED] open sets in R^2

    1. The problem statement, all variables and given/known data
    If A, B are open in R^2, and A is contained in the closure(B), then is it true that A is contained in B?


    2. Relevant equations



    3. The attempt at a solution
    It seems intuitively true.

    If a is in A, then there is a sequence b_n in B that converges to a by definition of closure. But I don't know what to do with that?
     
  2. jcsd
  3. Apr 24, 2008 #2

    Dick

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    It doesn't seem intuitively true to me. Take B=R^2-{(0,0)}. Give me a counterexample.
     
    Last edited: Apr 24, 2008
  4. Apr 24, 2008 #3
    any open set containing the origin
     
  5. Apr 24, 2008 #4

    Dick

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    Yep.
     
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