Paracompactness and metrizable manifolds

  1. Hi, where I can find a proof of the theorem that establishes that a manifold is metrizable (with a riemannian metric) if and only if is paracompact?.
    Last edited: May 15, 2011
  2. jcsd
  3. Wow, I found a proof in Kobayashi and Nomizu, Vol I, and it seems pretty hard :frown:. I think that simply I will have to accept the result :cry:
  4. micromass

    micromass 18,961
    Staff Emeritus
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    Hi aleazk! :smile:

    Try "topology" of Munkres, it gives an easy proof of the result (but the proof is still several pages long :smile: )
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