Notions de topologie : introduction aux espaces fonctionnels / Claude Tisseron

The present book consists of three chapters of which the first two serve as an introduction in the basic notions of point-set topology. Less elementary concepts and facts are treated in exercises for each section. For example, the Zariski topology on the set of all prime-ideals of a commutative ring with a unit is discussed and the fundamental group of a topological space is introduced. The third chapter is dedicated to the functional spaces. Normed and Hilbert spaces are discussed, many examples from analysis given. The following topics receive a detailed treatment: The Hahn-Banach theorem, the theorems of Gelfand-Mazur and Banach-Steinhaus and the open mapping theorem. Finally the closed graph theorem and certain facts concerning linear mappings are given as an application. (Zentralblatt)

Bibliogr. p. 307-308. Index