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Topologie et analyse fonctionnelle : cours de licence avec 240 exercices et 30 problèmes corrigés / Yves Sonntag

Auteur principal : Sonntag, Yves, AuteurType de document : MonographieCollection : UniversitésLangue : français.Pays : France.Éditeur : Paris : Ellipses, 1998Description : 1 vol. (512 p.) : ill. ; 26 cmISBN : 2729857141.ISSN : 1288-877X.Bibliographie : Bibliogr. p. [507]-508. Index.Sujet MSC : 00A07, General -- General and miscellaneous specific topics, Problem books
46-01, Functional analysis, Instructional exposition (textbooks, tutorial papers, etc.)
54-01, General topology, Instructional exposition (textbooks, tutorial papers, etc.)
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In spite of its general title, this is basically an elementary textbook on the theory and applications of metric spaces. It consists of 21 chapters with the following headings: 1. Distances and metric spaces; 2. Normes and normed linear spaces; 3. Point sequences in a metric space; 4. Density and approximation in a metric space; 5. Closed sets in a metric space; 6. Open sets in a metric space; 7. Continuous maps; 8. Uniformly continuous maps and homeomorphisms; 9. Products of metric spaces and continuity; 10. Continuous linear maps; 11. Cauchy sequences, complete metric spaces, Banach and Hilbert spaces; 12. Complete metric spaces (continued); 13. Compact metric spaces (I); 14. Compact metric spaces (II); 15. Completion of a metric space, a normed linear space, and a pre-Hilbert space; 16. Applications of complete metric spaces (I): fixed points; 17. Applications of complete metric spaces (II): projections; 18. Real Hilbert spaces (I): Riesz theorem and beyond; 19. Real Hilbert spaces (II): Hilbert bases; 20. Connectedness; 21. Minimization of a quadratic form. (Zentralblatt)

Bibliogr. p. [507]-508. Index

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