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?
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?
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.