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

Hausdorff condition in differential manifold definition

  1. Jul 2, 2010 #1
    Dear all,
    why is it needed in the diff manifold definition that the base set M is topologically Hausdorf ?
    Since M is locally homeomorphic with Rn as metric space is Hausdorf, shouldn't this condition be automatically satisfied?
    Thanks.
    Goldbeetle
     
  2. jcsd
  3. Jul 2, 2010 #2
    The line with two origins is locally Euclidean, but not Hausdorff.
     
  4. Jul 2, 2010 #3
    OK, true.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook