Two results about points, lines and planes
The results are: Given n points in \(E_ 3\) not all on a plane and determining \(\ell\) lines and p planes, it holds a) \(\ell^ 2\geq cnp\), \(c>0\), b) if not all points are contained in two skew lines, then there is a point (of the original ones) that is incident with at least \(b\ell\) of the (original) planes, where \(b>0\). - The results are related to two conjectures on the objects investigated. [Cf. \textit{J. Beck}, Combinatorica 3, 281-297 (1983; Zbl 0533.52004) and the author, Geom. Dedicata 10, 317-321 (1981; Zbl 0474.52013)].
scientific article; zbMATH DE number 3962626