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Math Help - Complex Variables

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    Complex Variables

    Prove that if a set contains each of its accumulation points, then it must be a closed set.
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    Quote Originally Posted by LCopper2010 View Post
    Prove that if a set contains each of its accumulation points, then it must be a closed set.
    Suppose that \mathcal{A} is such a set.
    If x\in\mathcal{A}^c, the complement, then x is not a limit point of \mathcal{A}.
    Therefore, the is an open set, x\in\mathcal{O}_x that contains no point of \mathcal{A}.
    Now show the complement is open.
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    What does this have to do with complex variables?
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