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Math Help - Open/Closed Sets - Complex Analysis

  1. #1
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    Open/Closed Sets - Complex Analysis

    Hey hey. I'm really struggling with this part of Complex analysis.

    Q. Which of these sets are open? closed? Justify your answer.
    (a) { z : Im(z) > 0 } ; (b) { z : Re(z) > 0, lzl<2 } ; (c) { z : lzl^2 <= 6 }

    I have to use the definition of open and closed sets to answer these 3 questions. I'm aware of the definitions, but don't really know how to apply them to problems. Any help would be appreciated. Thanks in advance.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by skamoni View Post
    Hey hey. I'm really struggling with this part of Complex analysis.

    Q. Which of these sets are open? closed? Justify your answer.
    (a) { z : Im(z) > 0 } ; (b) { z : Re(z) > 0, lzl<2 } ; (c) { z : lzl^2 <= 6 }

    I have to use the definition of open and closed sets to answer these 3 questions. I'm aware of the definitions, but don't really know how to apply them to problems. Any help would be appreciated. Thanks in advance.
    A set is open if for every point in the set it contains an open disk containing that point.

    a) if u in { z : Im(z) > 0 }, then the open disk |z-u|<Im(u)/2 is contained in the set, and so it is open. Also it is not closed as it is not equal to its closure { z : Im(z) >= 0 }

    CB
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