Ensembles de classe (0, 1, q,q + 1) de PG (d,q)

We determine all sets Q of points of any finite dimensional protective space P such that each line intersecting Q in more than one point, either is contained in Q or contains exactly one point not on Q. If P is a finite protective space of order q, these sets are the so called sets of class (0, 1, q, q + 1).