Raising the Differentiability Class of a Manifold in Euclidean Space

Let E Denote the Cuclidean (n+k)-space of Points X with Rectangular Cartesian Coordinates (x₁,, X₂, …, Xn+k). Let M be an n-dimensional Differentiable Manifold of Class C^m, M > 0, Regularly Imbedded in E.