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Math Help - Topology exercise.

  1. #1
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    Topology exercise.

    Picture attached.
    Attached Thumbnails Attached Thumbnails Topology exercise.-screen-shot-2012-10-17-9.13.28-pm.png  
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  2. #2
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    Re: Topology exercise.

    Quote Originally Posted by vercammen View Post
    Picture attached.
    You have posted an attachment without any comment whatsoever.
    Do you expect someone to do the problem(s) for you?
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  3. #3
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    Re: Topology exercise.

    I expect any kind of help. Even hint or the first step.
    Anyway, here is what I got

    1. Clearly \supset is always true, even when G is not open. Let x\in \overline{G\cap \overline A}, and O an open neighborh. of x. It necessarily meets a point of G\cap \overline A, say y. As y\in\overline A, and G is a neighborhood of y, G\cap A\cap O\neq \emptyset. So x\in \overline{G\cap A}.

    2. We consider the real line with usual topology, A:=(0,1) and G:=\{0\}. The LHS is \{0\} but the RHS is empty.
    Last edited by vercammen; October 30th 2012 at 11:49 PM.
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  4. #4
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    Re: Topology exercise.

    What are some good books for a layperson who wants to teach himself set theory?







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