Notions de topologie: introduction aux espaces fonctionnels / Claude Tisseron

Auteur: Tisseron, Claude - AuteurType de document: Monographie Collection: Collection méthodes Langue: françaisPays: FranceÉditeur: Paris : Hermann, 1985Description: 1 vol. (319 p.) : ill. ; 22 cm ISBN: 2705660194 ; br. Note: 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)Bibliographie: Bibliogr. p. 307-308. Index. Sujets MSC: 46-01 Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.)
54-01 General topology -- Instructional exposition (textbooks, tutorial papers, etc.)
46B03 Functional analysis -- Normed linear spaces and Banach spaces; Banach lattices -- Isomorphic theory (including renorming) of Banach spaces
46C05 Functional analysis -- Inner product spaces and their generalizations, Hilbert spaces -- Hilbert and pre-Hilbert spaces: geometry and topology
46A30 Functional analysis -- Topological linear spaces and related structures -- Open mapping and closed graph theorems; completeness (including B-, Br-completeness)
Location Call Number Status Date Due
Salle E 09237-01 / Manuels TIS (Browse Shelf) Available

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

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