Lower bounds for approximation by nonlinear manifolds

which is the precision to which F approximates K. An instance of classical interest is that in which L is C([O, 1]), K is AO-i.e. those functions bounded by one, and whose modulus of continuity is dominated by the modulus of continuity function w-and F is the family P,, of polynomials of degree n-1. For this case it is known that there are positive constants A and B, independent of w and n, such that