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Math Help - MAT322(Metric Space)

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    Thumbs up MAT322(Metric Space)

    If A1,A2,......An, is a collection of n number of sets in a metric space, prove that their intersection is open.
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    Re: MAT322(Metric Space)

    Quote Originally Posted by ajibolaadebisi View Post
    If A1,A2,......An, is a collection of n number of sets in a metric space, prove that their intersection is open.
    As written that statement is false.
    If each of the A_i is closed and \bigcap\limits_n {{A_n}}  \ne \emptyset then \bigcap\limits_n {{A_n}}  is closed.

    Did you mean each of the A_i is open?
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