Is every one-dimensional manifold orientable?

racoonlly · Nov 2, 2010

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

quasar987 · Nov 2, 2010

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.

Is every one-dimensional manifold orientable?

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Is every one-dimensional manifold orientable?

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