  Results are proved indicating that the Veronese map v_d often increases
independence of both sets of points and sets of subspaces. For example, any d+1
Veronesean points of degree d are independent. Similarly, the dth power map on
the space of linear forms of a polynomial algebra also often increases
independence of both sets of points and sets of subspaces. These ideas produce
d+1-independent families of subspaces in a natural manner.
