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@darijgrinberg Thank you for the reference. However, it's another kind of proof. I'm still curious why this part is true in Lang's book. I think this part is more complicated than I thought.
in fact, I'm yet an undergraduate student, I will begin my master classes in March. Thank you for your answer, I'm going to see this problem, thank you very much for your answer.
I've already studied the whole Lee's book Introduction of topological manifolds and some books of simplicial homology. Do you think I can understand the Milnor Stasheff's book, for example? Thank you for your answer.
