The generalized division lemma in the finitely differentiable case
Let 000 be the origin of Rm+1\Bbb R^{m+1}Rm+1, let yyy be its (m+1)(m+1)(m+1)-st coordinate, and let h∈Ck(Rm+1)h\in C^k(\Bbb R^{m+1})h∈Ck(Rm+1) satisfy … for some s≤ks\le ks≤k. Write Ck(Rm+1)(0)C^k(\Bbb R^{m+1})_{(0)}Ck(Rm+1)(0) for the…