Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.
Ce livre est le cinquieme du traite; il est consacre aux bases de l'analyse fonctionnelle. Il contient en particulier le theoreme de Hahn-Banach et le theoreme de Banach-Steinhaus. Il comprend les chapitres: -1. Espaces vectoriels topologiques sur un corps value; -2. Ensembles convexes et espaces localement convexes; -3. Espaces d'applications lineaires continues; -4. La dualite dans les espaces vectoriels topologiques; -5. Espaces hilbertiens (theorie elementaire).
Il contient egalement des notes historiques.
Ce volume a ete publie en 1981.
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