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Math Help - Hausdorff

  1. #1
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    Hausdorff

    how would I prove a subset x of Euclidean space with the usual topology is Hausdorff?
    I know that I need to show that for a pair of distinct points a,b in x there exists two open sets such that a in u and b in v and these two sets have no elements in common.....
    Not sure how to proceed...!
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  2. #2
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    Quote Originally Posted by bigdoggy View Post
    how would I prove a subset x of Euclidean space with the usual topology is Hausdorff?
    I know that I need to show that for a pair of distinct points a,b in x there exists two open sets such that a in u and b in v and these two sets have no elements in common.....
    Not sure how to proceed...!
    If a and b are distinct points then d(a,b)> 0. Look at the neighborhood centered on a with radius d(a,b)/3 and the neighborhood centered on b with radius d(a,b)/3.
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