Definition talk:Regular Value

The problem is that it is tedious and confusing for others to define pushforward without a rigorous definition of tangent spaces, tangent bundles and vector fields, which do not exist yet. The symbol $f_* \vert_x$ is a notation for "the pushforward of $f$ at $x$". After thinking a while, one could take $f_* \left(x\right)$ or $f_* \restriction_x$, but the latter produces a thick space and it is not really $f_*$ restricted to $x$, but $f_*$ evaluated at $x$ acting on tangent vectors. I read the house style page and tried sticking to it, which points did I not follow? I will try following it next time.--Geometry dude (talk) 20:00, 15 September 2014 (UTC)