Are All Manifolds Defined to Be Hausdorff?

[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 don't 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.

 

[pasmith]

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