## proving 1-dim manifold is orientable [closed]

I have the result that any 1 dim topological manifold is either $\mathbb{R}$ or $S^{1}$. And I have the fact that every 1-dim topological manifold is orientable in the sense of orientation on simplices.

i want to get that any 1-dim manifold (smooth) is orientable, where orientability is given by the existence of a nowhere vanishing 1-form. Since i know my manifold is either the real line or the circle, does the section $s: M \longrightarrow T^{*}M$ that takes each point p to the differential dx at p work as the 1-form i need?

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Not the right place for this question. – Alain Valette May 1 2011 at 8:26
While it's decidedly not the same question, mathoverflow.net/questions/54645/… is at least related. – Zsbán Ambrus May 1 2011 at 8:57
Yes . – Kevin Lin May 1 2011 at 9:29
Dear Jessica. You question looks like a homework problem. If that's the case, then MO is definitely not appropriate for that. – André Henriques May 1 2011 at 10:14
Dear Jessica, Since no-one else mentioned it, let me suggest math.stackexchange.com as an appropriate place to ask your question. Regards, Matthew – Emerton May 1 2011 at 15:26
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