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?
2026-05-14 14:23:18.1778768598
Every $1$-manifold is orientable
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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.