Let M1,..,Mk be smooth manifolds, and let Pi_j be the projection from M1XM2X...XMk->Mj. Show that the map a:T_(p1,...,pk)(M1XM2X...Mk)->T_p1(M1)[tex]\oplus[/tex]...[tex]\oplus[/tex]T_pk(Mk)(adsbygoogle = window.adsbygoogle || []).push({});

a(X)=(Pi_1*X,Pi_2*X,....,Pi_k*X) is an isomorphism.

The way I am thinking to prove the statement is to show that a is a bijection, since a is already a linear map. And I have no clue how to show it, help needed!

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