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Math Help - Interior point

  1. #1
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    Question Interior point

    Help me please. I can not prove the following.

    Prove that a point belongs to the lock of A if and only if is a interior point or a frontier point of A.

    Thanks
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  2. #2
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    Quote Originally Posted by osodud View Post
    Prove that a point belongs to the lock of A if and only if is a interior point or a frontier point of A.
    Some translations are in order here.
    ‘lock’ must mean closure; ‘frontier’ must mean boundary.

    A point is in the closure of the set iff every open set containing the point contains a point of the set.

    Thus, if we have a interior point or a frontier point of A then by definition it is in the closure.

    Suppose p\in \overline{A}, the closure.
    If p is an interior point of A we are done.
    So what does it mean to say that p is not an interior point?
    Now you need to consider two cases: p\in A~\&~p\notin A.
    Both cases should force p to be a boundary point.
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