Linear spaces with projective lines

A line L of a linear space (P) 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) 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 L_i,K_i ⊂ E_i 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 Ø ≠ G ∩ H₁ ≠ G ∩ H₂ ≠ Ø. Then the Bundle Theorem holds and (P,) is locally projective. Therefore (P,) is embeddable in a projective space (cf. Theorem 4.1).