# Open sets in R^2

[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?

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

Last edited:
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
Homework Helper
Yep.