View Single Post
quasar987
#10
Feb6-12, 02:57 PM
Sci Advisor
HW Helper
PF Gold
quasar987's Avatar
P: 4,771
Quote Quote by Identity View Post
Just to make sure I've got it, in

[tex][F_{*p}(X)](f) = X(f\circ F)[/tex]
[itex]f[/itex] is kind of placeholder, in the sense that the [itex]f[/itex] on the LHS is an arbitrary function in [itex]C^\infty(p)[/itex] and the [itex]f[/itex] on the RHS is an arbitrary function in [itex]C^\infty (F(p))[/itex]
The f in the LHS is the same as the f in the RHS, and in both case, it is a function in [itex]C^\infty (F(p))[/itex]. Indeed, it better be so that f o F is in [itex]C^\infty(p)[/itex] so that X(f o F) makes sense!