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

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