Elements of the Theory of Functions and Functional Analysis Volume 1 Metric and Normed Spaces

Cover S Title OTHER GRAYLOCK PUBLICATIONS Title: Elements of the Theory of Functionsand Functional Analysis, VOLUME 1, METRIC AND NORMED SPACES Copyright CONTENTS PREFACE TRANSLATOR'S NOTE 1 FUNDAMENTAL CONCEPTS OF SET THEORY §1. The concept of set. Operations on sets §2. Finite and infinite sets. Denumerability §3. Equivalence of sets §4. Nondenumerability of the set of real numbers §5. The concept of cardinal number §6. Partition into classes §7. Mappings of sets. General concept of function 2 METRIC SPACES §8. Definition and examples of metric spaces §9. Convergence of sequences. Limit points §10. Open and closed sets §11. Open and closed sets on the real line §12. Continuous mappings. Homeomorphism. Isometry §13. Complete metric spaces §14. Principle of contraction mappings and its applications § 15. Applications of the principle of contraction mappings in analysis §16. Compact sets in metric spaces §17. ArzeIa's theorem and its applications §18. Compacta §19. Real functions in metric spaces §20. Continuous curves in metric spaces 3 NORMED LINEAR SPACES §21. Definition and examples of normed linear spaces §22. Convex sets in normed linear spaces §23. Linear functionals §24. The conjugate space §25. Extension of linear functionals §26. The second conjugate space §27. Weak convergence §28. Weak convergence of linear functionals §29. Linear operators ADDENDUM TO CHAPTER ITI Generalized Functions 4 LINEAR OPERATOR EQUATIONS §30. Spectrum of an operator. Resolvents §31. Completely continuous operators §32. Ljnear operator equations. The Fredholm theorems LIST OF SYMBOLS LIST OF DEFINITIONS LIST OF THEOREMS BASIC LITERATURE INDEX