  Some properties of the (normed) dual Hom-functor $D$ and its iterations $D^n$
are exhibited. For instance: $D$ turns every canonical embedding (in the second
dual space) into a retraction (of the third dual onto the first one); $D$ rises
the countably infinite (algebraic) dimension only; $D$ does not change the
finite quotient shape type. By means of that, the finite quotient shape
classification of normed vectorial spaces is completely solved. As a
consequence, two extension type theorems are derived.
