  If $\phi: L\to L'$ is a bijection from the set of lines of a linear space
$(P,L)$ onto the set of lines of a linear space $(P',L')$ ($\dim P, \dim P'\geq
3$), such that intersecting lines go over to intersecting lines in both
directions, then $\phi$ is arising from a collineation of $(P,L)$ onto
$(P',L')$ or a collineation of $(P,L)$ onto the dual linear space of $(P',L')$.
However, the second possibility can only occur when $(P,L)$ and $(P',L')$ are
3-dimensional generalized projective spaces.

Algebraic Geometry