View Single Post

Recognitions:
Gold Member
Homework Help
 Quote by Identity Just to make sure I've got it, in $$[F_{*p}(X)](f) = X(f\circ F)$$ $f$ is kind of placeholder, in the sense that the $f$ on the LHS is an arbitrary function in $C^\infty(p)$ and the $f$ on the RHS is an arbitrary function in $C^\infty (F(p))$
The f in the LHS is the same as the f in the RHS, and in both case, it is a function in $C^\infty (F(p))$. Indeed, it better be so that f o F is in $C^\infty(p)$ so that X(f o F) makes sense!