I found this statement from my text very confusing:
What does it mean by identification of each tangent space $T_pV$ with $V$ itself? - what does "identification" really mean here?
If it means isomorphic, then it conflicts with my understanding that each tangent space $T_pV$ is locally isomorphic to $V$.
What is $Xf$? I don't understand the expression. I don't know what is the function $f$.
Thank you very much for your help.