in an affine space with the same point set is studied. On the other hand, it can be considered as an affine space with some lines deleted. As it was mentioned, an affine space is a complement of a projective space, and thus there is a correspondence between [@partaffine] and our research. To restore missing lines (and preserve parallelism) the authors introduce some additional combinatorial condition. Namely, all investigations in [@partaffine] are done under assumption, that on every line $k$, for any point $p\notin k$, there is more points collinear with $p$ than those not collinear with $p$. Likewise, we require that on every line of $\fixoutf(\A,\W)$ there is less points of $\W$ than the other.

Results
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The purpose of this paper is to give an answer to the above question for projective spaces and Grassmann spaces where a set of points, under some restrictions, has been removed. In the first part we focus on a projective space as $\A$. Purely in terms of the complement of $\W$ in $\A$ we reconstruct the removed points and lines as well as the relevant incidence. An affirmative answer to our question is given in Theorem \[thm:main-proj\].

In the second part we 