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Open sets in R^2

  • Thread starter ehrenfest
  • Start date
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[SOLVED] open sets in R^2

1. 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?


2. Homework 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?
 

Answers and Replies

Dick
Science Advisor
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It doesn't seem intuitively true to me. Take B=R^2-{(0,0)}. Give me a counterexample.
 
Last edited:
1,996
1
It doesn't seem intuitively true to me. Take B=R^2-{(0,0)}. Give me a counterexample.
any open set containing the origin
 
Dick
Science Advisor
Homework Helper
26,258
618
Yep.
 

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