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Math Help - Topological Groups

  1. #1
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    Topological Groups

    Urgent answer required!

    Q. Given topological groups X & Y, and homorphism f:X->Y, verify that the following are equivalent:
    (a) f is an open map
    (b) for each nhd N of e(x), f(N) is a nhd or e(y), e(x) is the identity
    (c) for each open nhd N of e(x), f(N) is a nhd of e(y)
    (d) for each open nhd N of e(x), f(N) is an open nhd of e(y)

    I know some of these are obvious but whats obvious to one person isn't always obvious to another.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Turloughmack View Post
    Urgent answer required!

    Q. Given topological groups X & Y, and homorphism f:X->Y, verify that the following are equivalent:
    (a) f is an open map
    (b) for each nhd N of e(x), f(N) is a nhd or e(y), e(x) is the identity
    (c) for each open nhd N of e(x), f(N) is a nhd of e(y)
    (d) for each open nhd N of e(x), f(N) is an open nhd of e(y)

    I know some of these are obvious but whats obvious to one person isn't always obvious to another.
    I fully answered one of your questions and ask you to show work on the other, but instead you just repost it.

    This is, as Plato would say, not a tutoring service. Let's see some work!
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