TITLE: "Abnormal" manifold
QUESTION [6 upvotes]: We often assume manifolds to be paracompact Hausdorff. Clearly, this implies normal.
However, there is a manifold (I mean locally Euclidean Hausdorff space) which is not paracompact. Without paracompactness, they are still regular because manifolds are locally compact, but does it imply normal?
The only example of non paracompact manifold which I know is the "long line". However, I hear this is normal. I want to know whether manifold implies normal or not.

REPLY [5 votes]: There are even non-normal separable complex manifolds. The paper Complex analytic manifolds without countable base by Calabi and Rosenlicht gives examples $M,S$ of a non-normal separable complex manifolds of complex dimension 2 and hence real dimension 4. It was proven by Rado that every Riemann surface is paracompact, so the dimension of these manifolds is optimal.