Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook