# Math Help - which is compact

1. ## which is compact

which of the following is compact and why? please explain how?
1) {(x,y):|x|<=1, |y|>=2}
2) {(x,y):|x|<=1, |y|^2>=2}
3) {(x,y):x^2+3y^2<=5}
4) {(x,y):x^2<=y^2 +5}

2. ## Re: which is compact

All you have to do is to apply the Heine Borel theorem. Just see the introduction to this wiki article: Heine . Draw the sets and see if they are closed and bounded.