ABSTRACT
In this chapter, we give some generalizations to Chapter 3 and also endeavor to provide sufficient background for discussion of ‘quasi-subgeometry’ partitions.
Definition 4.1. A ‘partial vector-space spread’ of a vector space V is merely a set of vector subspaces any two distinct elements of which direct sum to the vector space and are each isomorphic to a fixed subspace. In a similar manner, one may define a ‘partial projective spread’. The elements of a partial spread are called ‘components’. From a partial vector-space spread P, we may form a ‘translation net’ T (P) by taking the ‘points’ of the net to be the vectors and the ‘lines’ of the net to be the vector translates of the partial spread components.
