  We study to which extent the family of pairs of subspaces of a vector space
related to each other via intersection properties determines the vector space.
In another language, we study to which extent the family of vertices of the
building of a projective space related to each other via several natural
respective conditions involving the Weyl distance and incidence determines the
building. These results can be seen as generalizations of and variations on the
Fundamental Theorem of Projective Geometry.
