1. Dec 13, 2014 #1

   hideelo

   

   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.

    

   hideelo, Dec 13, 2014
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3. Dec 13, 2014 #2

   pasmith

   

   Homework Helper

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

    

   pasmith, Dec 13, 2014

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