Functional Topology and Abstract Variational Theory

This paper is concerned with a summary of results which will appear at length in a fasicule in the series "M6morial des sciences math6matiques," Gauthier-Villars, Paris.Part of the theory is based on certain conceptions and theorems in group theory.These will be summarized first in order to make clear their independence from the rest of the theory.1.The Group Theory.-LetG be an additive abelian operator group with coefficients a in a field A. With certain of the elements u of G we