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Math Help - which is compact

  1. #1
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    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}
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  2. #2
    Member ModusPonens's Avatar
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    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.
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