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Math Help - Topology on X

  1. #1
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    Topology on X

    Consider the set X=\{a,b,c\}

    The collection of subsets are \O,X,\{a,b\},\{b,c\},\{b\}

    The book says the one point set \{b\} is not closed because its complement is not open. What is the complement of \{b\}\mbox{?}
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    Re: Topology on X

    Quote Originally Posted by dwsmith View Post
    Consider the set X=\{a,b,c\}
    The collection of subsets are \O,X,\{a,b\},\{b,c\},\{b\}
    The book says the one point set \{b\} is not closed because its complement is not open. What is the complement of \{b\}\mbox{?}
    \color{blue}X\setminus\{b\}=\{a,c\}
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    Re: Topology on X

    Quote Originally Posted by Plato View Post
    \color{blue}X\setminus\{b\}=\{a,c\}
    But that isn't in topology.
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    Re: Topology on X

    Quote Originally Posted by dwsmith View Post
    But that isn't in topology.
    That is exactly the point.
    The complement of \{b\} is not an open set, not in the topology.
    There because the complement of \{b\} is not open means \{b\} is not closed.
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