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Two simple questions in topology.

  1. Dec 2, 2007 #1


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    Gold Member

    just want to see if i got these:
    1.let U be open in X and A closed in X then U-A is open in X and A-U is closed in X.
    2. if A is closed in X and B is closed in Y then AxB is closed in XxY.

    my proof:
    A'=X-A which is open in X
    X-(A-U)=Xn(A'U U)=A'U(U) but this is a union of open sets and thus it's open thus:
    A-U is closed.
    U'=X-U which is closed in X
    but this is an intersection of closed sets and thus it's also closed.
    which means that U-A is open.

    let's look at:
    now X-A is open in X and Y is open in Y so (X-A)xY is open in XxY the same for Xx(Y-B) so we have here that it equals an arbitrary union of open sets so it's also an open set, thus AxB.
  2. jcsd
  3. Dec 2, 2007 #2


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    Homework Helper
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    The only problem I see is that for question 2, you're leaving the reader to fill in some blanks like how you're going to solve the problem and the conclusion.

    Start like this...

    I will show that AxB is closed in XxY by showing XxY-AxB is open in XxY.

    See what I'm saying?

    I hate writing proofs and I suck at writing them, but I do know how to write them properly if I really really had to.
  4. Dec 3, 2007 #3


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    those are minute details, and usually in exams i do write the proofs properly, this is only a few questions from munkres (the easy ones) that im solving for myself.
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