Is every one-dimensional manifold orientable?

[racoonlly]

Is there any non-orientable one-dimensional manifold ? If not, how to prove it? Thanks!

 

[quasar987]

The standard way to go is to go ahead and prove that up to homeomorphism, the only 1- dimensional manifolds (without boundary) are the real line and the circle.

This is done in Lee's "Introduction to topological manifolds" for instance.