Topological Vector Spaces I | WorldCat.org (original) (raw)

Physical Description:1 online resource

ISBN:

9783642649882, 9783642649905, 3642649882, 3642649904

OCLC Number / Unique Identifier:840293704

Additional Physical Form Entry:

Contents:

One Fundamentals of General Topology.- § 1. Topological spaces.- § 2 . Nets and filters.- § 3. Compact spaces and sets.- § 4. Metric spaces.- § 5. Uniform spaces.- § 6. Real functions on topological spaces.- Two Vector Spaces over General Fields.- § 7. Vector spaces.- § 8. Linear mappings and matrices.- § 9. The algebraic dual space. Tensor products.- § 10. Linearly topologized spaces.- § 11. The theory of equations in E and E*.- § 12. Locally linearly compact spaces.- § 13. The linear strong topology.- Three Topological Vector Spaces.- § 14. Normed spaces.- § 15. Topological vector spaces.- § 16. Convex sets.- § 17. The separation of convex sets. The Hahn-Banach theorem.- Four Locally Convex Spaces. Fundamentals.- § 18. The definition and simplest properties of locally convex spaces.- § 19. Locally convex hulls and kernels, inductive and projective limits of locally convex spaces.- § 20. Duality.- § 21. The different topologies on a locally convex space.- § 22. The determination of various dual spaces and their topologies.- Five Topological and Geometrical Properties of Locally Convex Spaces.- § 23. The bidual space. Semi-reflexivity and reflexivity.- § 24. Some results on compact and on convex sets.- § 25. Extreme points and extreme rays of convex sets.- § 26. Metric properties of normed spaces.- Six Some Special Classes of Locally Convex Spaces.- § 27. Barrelled spaces and Montel spaces.- § 28. Bornological spaces.- § 29. (F)- and (DF)-spaces.- § 30. Perfect spaces.- § 31. Counterexamples.- Author and Subject Index.