Advanced prerequisite for E-infinity theory

This is the third of a series of papers written with the primary aim of communicating necessary theoretical background knowledge required for an in-depth study of E-infinity theory. Compared to the previous two papers [El Naschie MS. Elementary prerequisites for E-infinity (Recommended background readings in nonlinear dynamics, geometry and topology). Chaos, Solitons & Fractals 2006;30(3):579–605; El Naschie MS. Intermediate prerequisites for E-infinity theory. Chaos, Solitons & Fractals 2006;30(3):622–8], the present one may be described as advanced.