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Math Help - Topology question

  1. #1
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    Topology question

    Hey sorry for another post. I'm trying to do an assignment and I really don't understand this question

    A intersection B is compact. Let B a subset of R2, be as follows: B = { (x,y) in R2s.t. y = sin(1/x), x>0} U {0,0}.
    a. Is B closed?, open?, bounded?, compact?

    Can you please explain the answer to me, I'm lost. Thanks a lot
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  2. #2
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    Re: Topology question

    Quote Originally Posted by willywonk View Post
    A intersection B is compact. Let B a subset of R2, be as follows: B = { (x,y) in R2s.t. y = sin(1/x), x>0} U {0,0}.
    a. Is B closed?, open?, bounded?, compact?

    If I were you, I would look at the graph of y=\sin(1/x),~x>0.

    I must tell you that I find your questions rather odd.
    It is clear that set B is clearly not closed (look at the graph).
    Therefore it cannot be compact.
    It certainly is not open.

    As to the idea of bounded, that is not a usual concept considered in topology. But if by bounded you mean that the diameter is finite that clearly it is not bounded.

    All of that said, I have no idea what the given, A\cap B is compact, adds to this question.

    I think that you are burden with poor text material.
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  3. #3
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    Re: Topology question

    Do you know what any of the words "compact", "open", "closed", or "bounded" mean?
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