Paracompactness and metrizable manifolds


by aleazk
Tags: metrizable manifolds, paracompactness
aleazk
aleazk is offline
#1
May14-11, 11:27 PM
P: 20
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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aleazk
aleazk is offline
#2
May15-11, 02:06 AM
P: 20
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
micromass
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#3
May15-11, 08:10 AM
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P: 16,583
Hi aleazk!

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


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