Foundations of real and abstract analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York [u.a.]
Springer
1998
|
| Schriftenreihe: | Graduate texts in mathematics
174 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 311 - 315 |
| Beschreibung: | XIV, 322 S. |
| ISBN: | 0387982396 |
Internformat
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| 245 | 1 | 0 | |a Foundations of real and abstract analysis |c Douglas S. Bridges |
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| 490 | 1 | |a Graduate texts in mathematics |v 174 | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface ix
Introduction 1
I Real Analysis 9
1 Analysis on the Real Line 11
1.1 The Real Number Line 11
1.2 Sequences and Series 20
1.3 Open and Closed Subsets of the Line 35
1.4 Limits and Continuity 41
1.5 Calculus 53
2 Differentiation and the Lebesgue Integral 79
2.1 Outer Measure and Vitali s Covering Theorem 79
2.2 The Lebesgue Integral as an Antiderivative 93
2.3 Measurable Sets and Functions 110
II Abstract Analysis 123
3 Analysis in Metric Spaces 125
3.1 Metric and Topological Spaces 125
3.2 Continuity, Convergence, and Completeness 135
xiv Contents
3.3 Compactness 146
3.4 Connectedness 158
3.5 Product Metric Spaces 165
4 Analysis in Normed Linear Spaces 173
4.1 Normed Linear Spaces 174
4.2 Linear Mappings and Hyperplanes 182
4.3 Finite Dimensional Normed Spaces 189
4.4 The Lp Spaces 194
4.5 Function Spaces 204
4.6 The Theorems of Weierstrass and Stone 212
4.7 Fixed Points and Differential Equations 219
5 Hilbert Spaces 233
5.1 Inner Products 233
5.2 Orthogonality and Projections 237
5.3 The Dual of a Hilbert Space 252
6 An Introduction to Functional Analysis 259
6.1 The Hahn Banach Theorem 259
6.2 Separation Theorems 275
6.3 Baire s Theorem and Beyond 279
A What Is a Real Number? 291
B Axioms of Choice and Zorn s Lemma 299
C Pareto Optimality 303
References 311
Index 317
|
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| indexdate | 2024-07-09T18:14:43Z |
| institution | BVB |
| isbn | 0387982396 |
| language | German |
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| series2 | Graduate texts in mathematics |
| spelling | Bridges, Douglas S. Verfasser aut Foundations of real and abstract analysis Douglas S. Bridges New York [u.a.] Springer 1998 XIV, 322 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 174 Literaturverz. S. 311 - 315 Mathematical analysis Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 Graduate texts in mathematics 174 (DE-604)BV000000067 174 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007909436&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bridges, Douglas S. Foundations of real and abstract analysis Graduate texts in mathematics Mathematical analysis Analysis (DE-588)4001865-9 gnd |
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| title | Foundations of real and abstract analysis |
| title_auth | Foundations of real and abstract analysis |
| title_exact_search | Foundations of real and abstract analysis |
| title_full | Foundations of real and abstract analysis Douglas S. Bridges |
| title_fullStr | Foundations of real and abstract analysis Douglas S. Bridges |
| title_full_unstemmed | Foundations of real and abstract analysis Douglas S. Bridges |
| title_short | Foundations of real and abstract analysis |
| title_sort | foundations of real and abstract analysis |
| topic | Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematical analysis Analysis |
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