ABSTRACT
In this final chapter, we construct and explore briefly the direct limit space for our family of spaces, namely DaQ = lim{D*}. There are also colimit spaces Eqq, Foo^ Wqo^ Toq. We construct these too, and we consider the relationships among them. With minor exceptions, the results of Sections 9, 10, 12, and 13 remain true when we put k = oo. One consequence of particular interest is the construction of a fibration
(15A)
in which the transgression is multiplication by pr. Let p > 5, and for now think of the parameters n > 1 and r > 1 as fixed. By (9B) each
Dk for k > 1 comes with a map i : Dk-1 —>► Dk. We now attach subscripts to the *’s and we consider the entire sequence at once:
(15B)
Define = lim{D*}. Since ij is an equivalence below dimension 2npk+1 — 1 once j is > k , the same is true of the inclusion : Dk —► Dqq. A CW structure for Dqq is
which gives the same information as the description of the reduced homology of Dk in Theorem 9.1(i) (put k = oo in that description).
