# Paracompactness and metrizable manifolds

1. ### aleazk

70
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. ### aleazk

70
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. ### micromass

18,961
Staff Emeritus
Hi aleazk!

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