TITLE: Every $1$-manifold is orientable
QUESTION [5 upvotes]: How to prove that every $1$-manifold is orientable?
Can I use Zorn's Lemma and produce a maximal orientable manifold  that will have to be all M?

REPLY [4 votes]: There are two connected 1-dimensional manifolds. The circle and the real line. Both are obviously orientable because the volume forms $d\theta$ and $dx$ are non-vanishing.