Hausdorff condition in differential manifold definition

1. Jul 2, 2010

Goldbeetle

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?
Thanks.
Goldbeetle

2. Jul 2, 2010

zhentil

The line with two origins is locally Euclidean, but not Hausdorff.

3. Jul 2, 2010

OK, true.