On generalized projective spaces operating on sets (Q1365027)

This is a detailed study of the properties of skew-projective spaces, a notion introduced by the author in Ann. Univ. Saraviensis Ser. Math. 7, 1-36 (1996) and Geom. Dedicata 58, No. 1, 63-73 (1995; Zbl 0836.51011) that generalizes both groups and projective spaces, and includes spherical spaces as well as the ideal spaces (spaces of infinity) of skew-affine spaces (another notion introduced by the author). One such property, that generalizes the well-known property of projective spaces, is that all proper subspaces of a certain class of skew-projective spaces (``with cancellation rule'') are desarguesian.