Notions de topologie : introduction aux espaces fonctionnels / Claude Tisseron
Type de document : MonographieCollection : Collection méthodesLangue : français.Pays : France.Éditeur : Paris : Hermann, 1985Description : 1 vol. (319 p.) : ill. ; 22 cmISBN : 2705660194.ISSN : 0588-2303.Bibliographie : Bibliogr. p. 307-308. Index.Sujet 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)
| Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|
| CMI Salle E | Manuels TIS (Browse shelf) | Available | 09237-01 |
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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