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Math Help - Open or Closed?

  1. #1
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    Open or Closed?

    Let

    A=\left\{ (a,b)\in\mathbb{R}^{2}:\:0\leq a<3,\:0\leq b\leq5\right\}

    Determine whether A is open, closed or neither. What is the closure, interior and boundary of A?

    I was under the impression that the set is neither open nor closed, but am struggling to prove this.
    Last edited by Plato; June 22nd 2011 at 10:09 AM. Reason: LaTeX fix
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  2. #2
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    Re: Open or Closed?

    Quote Originally Posted by Cairo View Post
    Let
    A=\left\{ (a,b)\in\mathbb{R}^{2}:\:0\leq a<3,\:0\leq b\leq5\right\}
    Determine whether A is open, closed or neither. What is the closure, interior and boundary of A?
    True or false: (3,5)\in A~?

    Can you show that (3,5)\in\beta(A), the boundary of A.
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  3. #3
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    Re: Open or Closed?

    you might want to consider the following subsets of \mathbb{R}^2:

    {0}x[0,5], {3}x[0,5], [0,3]x{0}, [0,3]x{5}.

    which of these are entirely in A?
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