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Hausdorff property of Manifolds

  1. Dec 13, 2014 #1
    Is the fact that all manifolds are hausdorff spaces a part of the definition, or can this be proven from the fact that it is a set which is locally isomorphic to open subsets of a hausdorff space?

    P.S. if it can be proven I dont want to know the proof, I want to keep working on it, I just want to know that hausdorff property is not some assertion put in from the outset.
  2. jcsd
  3. Dec 13, 2014 #2


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    The Hausdorff requirement is part of the definition of a topological manifold. There exist non-Hausdorff spaces which are locally homeomorphic to Euclidean spaces.
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