Grassmann space associated with a planar space.

A planar space is a triple Π=(S,L,P), where (S,L) is a linear space, and P is a family of proper subspaces of (S,L) (the planes), such that three points not on a line are contained in a unique plane, and every plane properly contains a line. Since the planes are defined, so are the pencils of lines and in this paper the Grassmann space Γ=(L,R), associated to a planar space is studied. Here R denotes the collection of all pencils of lines. This Γ is a partial line space, where "partial'' means that there exist pairs of points (elements of L) which are joined by no line (element of R). A star is the set of all lines of Π through a point. So a star also is a maximal subspace of Γ.