# Math Help - Closed sets

1. ## Closed sets

Which of these sets are closed in $\mathbb{R}^2$?
A) {<x,y>|x+y=1}
B) {<x,y>|x+y>1}

2. Originally Posted by tarheelborn
Which of these sets are closed in $\mathbb{R}^2$?
A) {<x,y>|x+y=1}
B) {<x,y>|x+y>1}
Here is a hint.
The A set is the boundary of the B set.

3. So I am thinking that the A set is closed but the B set is open because boundaries are the "problem" areas for open sets. Right?

4. An open set contains no boundary points.

5. Right, so B would be open because I can define an open ball such that for every x in B there is delta > 0 so that B[x; delta] is contained in B. The same could not be said of A because if we let x=1 there is no delta small enough to contain an open ball at x with radius delta. Is that more or less how a proof should go?