I'm looking to prove the Global Frobenius theorem, however in order to do so I need to prove the following lemma:(adsbygoogle = window.adsbygoogle || []).push({});

If ##D## is an involutive distribution and and ##\left\{N_\alpha\right\}## is collection of integral manifolds of ##D## with a point in common, then ##N = \cup_\alpha N_{\alpha}## has a unique smooth structure making it into connected integral manifold of ##D## in which each ##N_\alpha## is an open submanifold.

Do you know somewhere where it is proved? Or can you help me prove it?

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# Uniqueness of smooth structure

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