Thread: Closed sets

Which of these sets are closed in ?
A) {<x,y>|x+y=1}
B) {<x,y>|x+y>1}

Originally Posted by tarheelborn

Which of these sets are closed in ?
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.

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?

An open set contains no boundary points.

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?