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Math Help - Hausdorffness!

  1. #1
    Newbie Throughpoint's Avatar
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    Hausdorffness!

    Hi, I'm having trouble with this problem class question. I literally have no idea where to begin.

    Prove that every metric space is a Hausdorff topological space.

    Thanks for any help whatsoever. =)
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  2. #2
    MHF Contributor

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    Shouldn't it be "Hausdorffity"?

    Given two points, p and q, let d= d(p,q), the distance between p and q as measured by the metric. Consider the sets N_{d/3}(p)= \{x| d(p, x)< d/3\} and N_{d/3}(q)= \{y| d(q, y)< d/3\}. Suppose z is contained in both of those sets and apply the triangle inequality to point p, q, and z.
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  3. #3
    Newbie Throughpoint's Avatar
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    Nov 2010
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    Nay, my professor repeatedly uses "Hausdorffness" in lectures! =D He's German though.. English isn't his first language..

    Anyways, thanks so much! I think I can crack it now.
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