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Math Help - Closed sets

  1. #1
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    Closed sets

    Which of these sets are closed in \mathbb{R}^2?
    A) {<x,y>|x+y=1}
    B) {<x,y>|x+y>1}
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  2. #2
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    Quote Originally Posted by tarheelborn View Post
    Which of these sets are closed in \mathbb{R}^2?
    A) {<x,y>|x+y=1}
    B) {<x,y>|x+y>1}
    Here is a hint.
    The A set is the boundary of the B set.
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  3. #3
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    So I am thinking that the A set is closed but the B set is open because boundaries are the "problem" areas for open sets. Right?
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    An open set contains no boundary points.
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    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?
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