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Is every one-dimensional manifold orientable?

  1. Nov 2, 2010 #1
    Is there any non-orientable one-dimensional manifold ? If not, how to prove it? Thanks!
  2. jcsd
  3. Nov 2, 2010 #2


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    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.
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