ABSTRACT
15.1. It is a great mistake to think of the subject of holomorphic mappings of infinite dimensional spaces as being a mere generalization of one or several complex variables. Deep new phenomena and profound and as yet unsolved problems present themselves naturally in the study of infinite dimensional holomorphy. The concept of radius of boundedness which we study in this chapter has no meaningful counterpart in finite dimensional holomorphy. We first study the convergence of Taylor series before introducing the concept of radius of boundedness. We also present a brief introduction to sub-harmonic and plurisubharmonic functions and their relationship with radius of boundedness.
