Chowʹs theorem for linear spaces Original Research Article

If ϕ : L→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,L), dim(P′,L′)⩾3), such that intersecting lines go over to intersecting lines in both directions, then ϕ 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.