ABSTRACT
In the last chapter, we made a purely algebraic study of (partial) spreadsets, treating them as sets of linear mappings. Here we consider the ‘geometry’ of (partial) spreadsets. More precisely, we describe a procedure that assigns to each (partial) spreadset r a (partial) spread V(r), regarded as being coordinatized by r. We consider several basic (but unsurprising) connections between r and V(r). For example, we verify that the kernel of the spreadset r may be identified with the kernel of V(r), and V(r) is Desarguesian if and only if the associated spreadset r is Desarguesian in the sense of the previous chapter. Likewise, it is shown that the Knuth semifield spreads, as well as all of the spreads introduced in chapter 3, yield non-Desarguesian spreads.
