Handbook of Analysis and Its Foundations (eBook)

Eric Schechter (Autor)

eBook Download: PDF | EPUB

1996 | 1. Auflage
883 Seiten
Elsevier Science (Verlag)
978-0-08-053299-8 (ISBN)

Infos

Eric Schechter obtained his Ph.D. in mathematics at the University of Chicago. He is currently Associate Professor at Vanderbilt University, and has also taught at Duke University. Schechters research focuses on differential equations, fixed point theory, and the Axiom of Choice. He currently resides in Nashville, Tennessee with his wife, Elvira Casal, and his two children. Please visit the web page for hisbook: http://math.vanderbilt.edu/-schectex/ccc/

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Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. - Covers some hard-to-find results including:- Bessagas and Meyers converses of the Contraction Fixed Point Theorem- Redefinition of subnets by Aarnes and Andenaes- Ghermans characterization of topological convergences- Neumanns nonlinear Closed Graph Theorem- van Maarens geometry-free version of Sperners Lemma- Includes a few advanced topics in functional analysis- Features all areas of the foundations of analysis except geometry- Combines material usually found in many different sources, making this unified treatment more convenient for the user- Has its own webpage: http://math.vanderbilt.edu/

Inhalt

Front Cover 1
Handbook of Analysis and Its Foundations 4
Copyright Page 5
Contents 8
Preface 14
PART A: SETS AND ORDERINGS 24
Chapter 1. Sets 26
Chapter 2. Functions 57
Chapter 3. Relations and Orderings 72
Chapter 4. More about Sups and Infs 101
Chapter 5. Filters, Topologies, and Other Sets of Sets 123
Chapter 6. Constructivism and Choice 154
Chapter 7. Nets and Convergences 178
PART B: ALGEBRA 200
Chapter 8. Elementary Algebraic Systems 202
Chapter 9. Concrete Categories 231
Chapter 10. The Real Numbers 265
Chapter 11. Linearity 295
Chapter 12. Convexity 325
Chapter 13. Boolean Algebras 349
Chapter 14. Logic and Intangibles 367
PART C: TOPOLOGY AND UNIFORMITY 430
Chapter 15. Topological Spaces 432
Chapter 16. Separation and Regularity Axioms 458
Chapter 17. Compactness 476
Chapter 18. Uniform Spaces 504
Chapter 19. Metric and Uniform Completeness 522
Chapter 20. Baire Theory 553
Chapter 21. Positive Measure and Integration 570
PART D: TOPOLOGICAL VECTOR SPACES 596
Chapter 22. Norms 598
Chapter 23. Normed Operators 630
Chapter 24. Generalized Riemann Integrals 652
Chapter 25. Fréchet Derivatives 684
Chapter 26. Metrization of Groups and Vector Spaces 711
Chapter 27. Barrels and Other Features of TVS's 744
Chapter 28. Duality and Weak Compactness 775
Chapter 29. Vector Measures 808
Chapter 30. Initial Value Problems 837
References 862
Index and Symbol List 880

Produkt-Details

• Erscheint lt. Verlag: 24.10.1996
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Personalwesen
• ISBN-10: 0-08-053299-3 / 0080532993
• ISBN-13: 978-0-08-053299-8 / 9780080532998