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Hausdorff condition in differential manifold definition

  1. Jul 2, 2010 #1
    Dear all,
    why is it needed in the diff manifold definition that the base set M is topologically Hausdorf ?
    Since M is locally homeomorphic with Rn as metric space is Hausdorf, shouldn't this condition be automatically satisfied?
  2. jcsd
  3. Jul 2, 2010 #2
    The line with two origins is locally Euclidean, but not Hausdorff.
  4. Jul 2, 2010 #3
    OK, true.
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