Abstract :
A line L of a linear space (P,L) is a projective line, if L intersects every line G of the plane L∪{x} for every x∈P⧹L. In this paper a linear space (P,L) with projective lines is considered. We assume that for any two planes E1,E2 which intersect in a line G, there are two projective lines Li,Ki⊂Ei with distinct intersection points p=L1∩L2, q=K1∩K2∈G. Furthermore, it is assumed that for two intersecting lines H1,H2 of a plane F and a point x∈F there exists a line G through x with ∅≠G∩H1≠G∩H2≠∅. Then the Bundle Theorem holds and (P,L) is locally projective. Therefore (P,L) is embeddable in a projective space (cf. Theorem 4.1).
