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Math Help - set closed but not compact

  1. #1
    Member thaopanda's Avatar
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    set closed but not compact

    need some help with this...

    Consider the set P := {(x,y) \epsilon R^2 : y^2 = 2x}. Show that P is closed in R^2 but not compact.

    thanks in advance!!
    Nicole
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  2. #2
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    Quote Originally Posted by thaopanda View Post
    need some help with this...

    Consider the set P := {(x,y) \epsilon R^2 : y^2 = 2x}. Show that P is closed in R^2 but not compact.

    thanks in advance!!
    Nicole
    P is closed because the polynomial f(x,y)=y^2-2x is continuous (everywhere) and P=f^{-1}(0). the reason that P is not compact is that it's clearly not bounded.
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