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Paracompactness and metrizable manifolds

  1. May 14, 2011 #1

    aleazk

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    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
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  3. May 15, 2011 #2

    aleazk

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    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. May 15, 2011 #3

    micromass

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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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