Some applications of the P-X dual

This dissertation is devoted to demonstrating how P-X duality may be used to obtain results on typesets and cotypesets of finite rank torsion free abelian groups. It is shown how P-X duality allows questions about the typeset of a group to be replaced by questions about the cotypeset of the dual group and how questions about the cotypeset of a group may be replaced by questions about the typeset of the dual group.

Specifically, using P-X duality, new proofs are given of the Cotype theorem and Ito's theorem which show that these theorems are equivalent.