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?.
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Paracompactness and metrizable manifolds
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Wow, I found a proof in Kobayashi and Nomizu, Vol I, and it seems pretty hard 
. I think that simply I will have to accept the result 
. I think that simply I will have to accept the result - 22,170
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Hi aleazk! 
Try "topology" of Munkres, it gives an easy proof of the result (but the proof is still several pages long )
Try "topology" of Munkres, it gives an easy proof of the result (but the proof is still several pages long
)