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Math Help - Two problems about openess

  1. #1
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    Two problems about openess

    Show that  S = \{ (x,y) \in \mathbb {R}^2 : xy > 1 \} and  C = \{ x \in \mathbb {R}^n : d(x,y) < 1 \ , \ y \in B , B being any set, are open.

    I understand that for both problems I need to pove that D(x, t ) are subsets of S and C for some positive number t. But, in the first one, I don't know how to get the y involve.

    For the second one, I have w in D(x,a), then |w-y| = |w-x+x-y| < |w-x| + |x-y| = |w-x| + 1, but then... how do I get it < 1?
    Last edited by tttcomrader; June 6th 2008 at 01:04 PM.
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  2. #2
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    Please edit your post. There is a LaTeX error.
    We don't know what B is. Please tell us.
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  3. #3
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    edited, thank you
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