@Bin Yu, thank you for your comments

there are examples of compact hausdorff topological space with a sequence which does not have a convergent subsequence. so a subnet of this sequence can not be considered as a subsequence. Now a question:Assume that X is a compact Hausdorff topological space such that every sequence has a convergent subsequence. Does it implies that X is first countable?

Is the answer to the original qustion obvious for commutative C* algebras?

"smoothness of the quotient map" is not a consequence of "rank theorem"?

@Bin Yu, thanks a lot for your answer I learn a lot from yor explaination. But I do not underestand some thing for example "there is a closed curve in S^3 which intersect torus in one point, this is a contradiction since H^1(S^3) is trivial".I have another question about your answer:with a compactness argument you said that the holonomy orbit of each point on transversal section, is a finite set, but it does not implies that the holonomy is trivial. Am I missing something?

@J Martel. Thank you very much for your answer. Regarding your last statement I think that every compact codimension one submanifold of R^n is oriantable and separating.If I remember well I saw this theorem some years ago in Hirsch "Differential Topology"

@J.Martel as a combination of your idea and Bin's proof it seems that we can conclude " A codimension one foliation of an open manifold with compact leaves, gives a trivial bundle" Am i write? is it a known theorem in foliation theory? However some part of Bin's proof is not clear for me: How is the open set U(T) constructed? what was the role of contractibility of T-l\cup m?

Thank you, could you please give me some references? Another question:should I underestand from your answer that lie algebra coefficients does not contain new information to study the homotopy type of a topological space?