@ACuriousMind You mentioned something about non-Hausdorff manifolds having very little relevance in physics the other day. I'm currently reading about the
Taub-NUT space in HE and some interesting non-Hausdorff properties arise. Further discussion is found in: Hajiek, P. (1971), 'Causality in non-Hausdorff space-times',
Comm. Math. Phys. 21, 75-84.