Open sets in R^2

1. Apr 24, 2008

ehrenfest

[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. Apr 24, 2008

Dick

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

Last edited: Apr 24, 2008
3. Apr 24, 2008

ehrenfest

any open set containing the origin

4. Apr 24, 2008

Yep.