Show it is always possible to find an atlas {Ci} of a differentiable manifold M, such that every Ui = R^n.

Where Ui is the domain of the chart Ci : Ui --> Mi

and

Mi is the subset of M such that union of Mi = M,

R^n is the n-dimensional euclidean space.

Remark: the manifold is a general manifold, not necessarily in R^m.