Paracompactness and metrizable manifolds

[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?.

[aleazk]

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:

[micromass]

Hi aleazk! :smile:

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