Open sets in R^2: Are open sets contained in their closures?

[ehrenfest]

[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?

 

[Dick]

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

 

[ehrenfest]

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]

Yep.