Paracompactness and metrizable manifolds

1. May 14, 2011

aleazk

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. May 15, 2011

aleazk

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

3. May 15, 2011

micromass

Staff Emeritus
Hi aleazk!

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