Incidence manifolds (Q749867)

The h-th Grassmann space associated with a projective space P is the incidence structure induced on the set of h-flats in P by the residues of all (h-1)-flats and all \((h+1)\)-flats in P by the residues of all (h-1)- flats and all \((h+1)\)-flats and their intersections. Segre's product space associated with two projective spaces consists of the cartesian product \(P_ 0\times P_ 0'\) of the point sets together with all sets of the form \(\{\) \(p\}\times X\) and \(X\times \{p\}\) where p is a point and X is a line or the entire point set of one factor. The paper under review survey and complements various axiomatic characterizations of these objects, both as incidence structures and as topological incidence structures (the latter corresponding to topological projective spaces).