Elements of the Theory of Functions and Functional Analysis

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More About This Textbook

Overview


Based on the authors' courses and lectures, this two-part advanced-level text is now available in a single volume. Topics include metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, and more. Each section contains exercises. Lists of symbols, definitions, and theorems. 1957 edition.
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Product Details

  • ISBN-13: 9780486406831
  • Publisher: Dover Publications
  • Publication date: 2/16/1999
  • Series: Dover Books on Mathematics Series
  • Edition description: Unabridged
  • Pages: 288
  • Sales rank: 704,746
  • Product dimensions: 5.40 (w) x 8.47 (h) x 0.52 (d)

Table of Contents

Preface
Translator's Note
CHAPTER I FUNDAMENTALS OF SET THEORY
1. The Concept of Set. Operations on Sets
2. Finite and Infinite Sets. Denumerability
3. Equivalence of Sets
4. The 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
CHAPTER II 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. The Principle of Contraction Mappings and its Applications
15. Applications of the Principle of Contraction Mappings in Analysis
16. Compact Sets in Metric Spaces
17. ArzelĂ 's Theorem and its Applications
18. Compacta
19. Real Functions in Metric Spaces
20. Continuous Curves in Metric Spaces
CHAPTER III 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 III GENERALIZED FUNCTIONS
CHAPTER IV LINEAR OPERATOR EQUATIONS
30. Spectrum of an Operator. Resolvents
31. Completely Continuous Operators
32. Linear Operator Equations. Fredholm's Theorems
LIST OF SYMBOLS
LIST OF DEFINITIONS
LIST OF THEOREMS
BASIC LITERATURE
INDEX
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