Open sets in R^2

  • Thread starter ehrenfest
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  • #1
ehrenfest
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[SOLVED] open sets in R^2

Homework Statement


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?


Homework Equations





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?
 

Answers and Replies

  • #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:
  • #3
ehrenfest
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It doesn't seem intuitively true to me. Take B=R^2-{(0,0)}. Give me a counterexample.

any open set containing the origin
 
  • #4
Dick
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Yep.
 

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