ABSTRACT
PR24 A subset W ofMn • defined by m equations/(x) = 0 and f having rank m at each point of W, is an (n-m)-dimensional differentiable submanifold ofMn.
Proof Let (V,rp) be a chart of Mn containing a point Xo E W . Putting
the assumption of rank m amounts to saying that the matrix
(oJi)ox' i =l,...,n;} =l,...,m has a Jacobian D(f~) (i,} = l, ...,m) different from zero.
