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Math Help - 2 questions in TOPOLOGY

  1. #1
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    2 questions in TOPOLOGY

    please:
    I need your help in these 2 Qs:
    the picture2 questions in TOPOLOGY-untitled.gif
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  2. #2
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    The first problem is proved in two steps.
    First, If B is a compact set and p\notin B then there are two disjoint open sets such B\subset G~\&~p\in H.

    Second, each point in A is not in B.
    If a\in A use part one to get disjoint open sets G_a~\&~H_a.
    The compactness of A gives a finite collection of each.
    The intersection of the G_x's is open and contains B.

    Problem #2. Use the co-finite topology to show it is false.
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  3. #3
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    thank u
    but could u please clear the second question more
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by rqeeb View Post
    thank u
    but could u please clear the second question more
    He's suggesting that you take \mathbb{R} with the cofinite topology. The important thing being that the resulting top. space isn't first countable.
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