e/Rank (differential topology)

Information
has gloss	eng: In mathematics, the rank of a differentiable map f : M → N between differentiable manifolds at a point p ∈ M is the rank of the derivative of f at p. Recall that the derivative of f at p is a linear map :Df_p : T_p M \to T_f(p)}N\, from the tangent space at p to the tangent space at f(p). As a linear map between vector spaces it has a well-defined rank, which is just the dimension of the image in Tf(p)N: :\operatornamerank}(f)_p = \dim(\operatornameim}(Df_p)).
lexicalization	eng: rank
instance of	e/Smooth function