How do I prove a set in R² is open using open balls?

[jdinatale]

I typed the question and my attempt at a solution below...

It seems obviously open to me, but I'm not sure how to state it using open balls considering that it's in R^2.

 

[SteveL27]

I typed the question and my attempt at a solution below...

It seems obviously open to me, but I'm not sure how to state it using open balls considering that it's in R^2.

If it's open, its complement is closed. What happens if you sneak up to it from above? Or below?