its geometric hyperplane yields an affine polar space (cf. [@cohenshult], [@afpolar], [@csaffpolar]). In a Grassmann space, in other words, in a space of pencils, this construction produces an affine Grassmannian (cf. [@cuypers]). When $\W$ is any subspace, not necessarily a hyperplane, in a projective space $\A$, then so called slit space arises as the complement $\fixoutf(\A,\W)$ possessing both projective and affine properties (cf. [@KM67], [@KP70]).

In [@kradzisz] (see also [@kradzisz2]) there is introduced an axiom system of semiaffine partial linear spaces (SAPLS in short) that are, without going into details, weak geometries with parallelism. It is astonishing that the set of directions of lines in a SAPLS form a subspace $\W$ of some projective space $\A$ so, we can treat this SAPLS as the complement $\fixoutf(\A,\W)$. More precisely, it is proved in [@kradzisz], that the class of semiaffine linear spaces coincides with the class of forementioned slit spaces. In other words, semiaffine linear spaces are slit spaces with parallelism that is not necessarily reflexive.

Another remarkable example is a spine space (cf. [@spinesp], [@autspine]), that emerges from a Grassmann space over a vector space by taking only those points which as $k$-dimensional vector subspaces meet a fixed vector subspace $W$ 