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