We can express every k-form in the form $ \omega(x) = \sum_Id_Idx_I $ where $ I$ is k-tuple and $ d_I$ is just some scalar function of x. That's entirely understandable for me. But while reading Munkres "Analysis on manifolds" I stumbled upon something quite confusing. In the discussion of the pullback function $ \alpha^*$, there is the following part: The form $ \alpha_*(dy_I)$ is a k-form defined on an open set of $ R^k$, so it has the form $ h dx_1\wedge dx_2 \wedge ... \wedge dx_k$ for some scalar function $ h $.
I completely don't see where that comes from. Can somebody clear this up for me?
Here are 2 pages of the book, puttin the problem in context: http://img31.imageshack.us/img31/5096/outfp.png