Visibility and parallelotopes in projective space

It is shown that if is a finite set of points in an ordered d-dimensional projective space, d2 and if all the hyperplanes spanned by points of are considered, then every such a hyperplane is visible from at most 2^d distinct points of ; if a hyperplane bounds 2^d distinct residences, then it contains exactly d points of . These results have been proved previously for d=2 and d=3.This paper is a revised version of results presented at the Conference on Geometry held at the University of Haifa (Israel), March. 10–13 (1975), 6].