# 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, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis54-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology

46B03, Functional analysis - Normed linear spaces and Banach spaces; Banach lattices, Isomorphic theory 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 Item type: Monographie

Current library | Call number | Status | Date due | Barcode |
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CMI Salle E | Manuels TIS (Browse shelf(Opens below)) | 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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