In this paper, we study the Grassmannian of n-dimensional subspaces of a
2n-dimensional vector space and its infinite-dimensional analogues. Such a
Grassmannian can be endowed with two binary relations (adjacent and distant),
with pencils (lines of the Grassmann space) and with so-called Z-reguli. We
analyse the interdependencies among these different structures.Comment: Correction of two typo
