Constructive analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1985
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
279 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 477 S. |
| ISBN: | 0387150668 3540150668 9783642649059 |
Internformat
MARC
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| 100 | 1 | |a Bishop, Errett |d 1928-1983 |e Verfasser |0 (DE-588)120476630 |4 aut | |
| 245 | 1 | 0 | |a Constructive analysis |c Errett Bishop ; Douglas Bridges |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1985 | |
| 300 | |a XII, 477 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 279 | |
| 650 | 7 | |a Analyse (wiskunde) |2 gtt | |
| 650 | 4 | |a Analyse mathématique - Fondements | |
| 650 | 7 | |a Constructieve wiskunde |2 gtt | |
| 650 | 7 | |a Grondslagen |2 gtt | |
| 650 | 4 | |a Mathematical analysis |x Foundations | |
| 650 | 0 | 7 | |a Konstruktive Analysis |0 (DE-588)4473957-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Konstruktive Analysis |0 (DE-588)4473957-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Bridges, Douglas S. |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-006128465 | ||
Datensatz im Suchindex
| _version_ | 1804123660766674944 |
|---|---|
| adam_text | Contents
Prolog 1
Chapter 1 A Constructivist Manifesto 4
1. The Descriptive Basis of Mathematics 4
2. The Idealistic Component of Mathematics 6
3. The Constructivization of Mathematics 9
Notes 13
Chapter 2 Calculus and the Real Numbers 14
1. Sets and Functions 14
2. The Real Number System 18
3. Sequences and Series of Real Numbers 28
4. Continuous Functions 35
5. Differentiation 44
6. Integration 50
7. Certain Important Functions 55
Problems 62
Notes 64
Chapter 3 Set Theory 67
1. Some Basic Notions of the Theory of Sets 67
2. Complemented Sets 72
3. Neighborhood Spaces and Function Spaces 75
Problems 78
Notes 79
Chapter 4 Metric Spaces 81
1. Fundamental Definitions and Constructions 81
2. Associated Structures 87
3. Completeness 89
4. Total Boundedness and Compactness 94
Contents XI
5. Spaces of Functions 100
6. Locally Compact Spaces 109
Problems 121
Notes 125
Chapter 5 Complex Analysis 128
1. The Complex Plane 128
2. Derivatives 130
3. Integration 134
4. The Winding Number 142
5. Estimates of Size, and the Location of Zeros 152
6. Singularities and Picard s Theorem 163
7. The Riemann Mapping Theorem 180
Problems 210
Notes 213
Chapter 6 Integration 215
1. Integration Spaces 216
2. Complete Extension of an Integral 222
3. Integrable Sets 232
4. Profiles 236
5. Positive Measures on IR 245
6. Approximation by Compact Sets 252
7. Measurable Functions 259
8. Convergence of Functions and Integrals 265
9. Product Integrals 277
10. Measure Spaces 282
Problems 292
Notes 297
Chapter 7 Normed Linear Spaces 299
1. Definitions and Examples 299
2. Finite Dimensional Spaces 306
3. The Lp Spaces and the Radon Nikodym Theorem 313
4. The Extension of Linear Functionals 334
5. Quasinormed Linear Spaces; the Space Lx 342
6. Dual Spaces 350
7. Extreme Points 357
8. Hilbert Space and the Spectral Theorem 363
Problems 390
Notes 396
XII Contents
Chapter 8 Locally Compact Abelian Groups 399
1. Haar Measure 399
2. Convolution Operators 419
3. The Character Group 424
4. Duality and the Fourier Transform 434
Problems 447
Notes 449
Chapter 9 Commutative Banach Algebras 450
1. Definitions and Examples 450
2. Linear Equations in a Banach Algebra 453
Problems 461
Notes 462
References 463
Symbols 467
Index 470
|
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| author | Bishop, Errett 1928-1983 Bridges, Douglas S. |
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| ctrlnum | (OCoLC)11867055 (DE-599)BVBBV009218539 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009218539 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:33:18Z |
| institution | BVB |
| isbn | 0387150668 3540150668 9783642649059 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006128465 |
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| physical | XII, 477 S. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Bishop, Errett 1928-1983 Verfasser (DE-588)120476630 aut Constructive analysis Errett Bishop ; Douglas Bridges Berlin [u.a.] Springer 1985 XII, 477 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 279 Analyse (wiskunde) gtt Analyse mathématique - Fondements Constructieve wiskunde gtt Grondslagen gtt Mathematical analysis Foundations Konstruktive Analysis (DE-588)4473957-6 gnd rswk-swf Konstruktive Analysis (DE-588)4473957-6 s DE-604 Bridges, Douglas S. Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-61667-9 Grundlehren der mathematischen Wissenschaften 279 (DE-604)BV000000395 279 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006128465&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bishop, Errett 1928-1983 Bridges, Douglas S. Constructive analysis Grundlehren der mathematischen Wissenschaften Analyse (wiskunde) gtt Analyse mathématique - Fondements Constructieve wiskunde gtt Grondslagen gtt Mathematical analysis Foundations Konstruktive Analysis (DE-588)4473957-6 gnd |
| subject_GND | (DE-588)4473957-6 |
| title | Constructive analysis |
| title_auth | Constructive analysis |
| title_exact_search | Constructive analysis |
| title_full | Constructive analysis Errett Bishop ; Douglas Bridges |
| title_fullStr | Constructive analysis Errett Bishop ; Douglas Bridges |
| title_full_unstemmed | Constructive analysis Errett Bishop ; Douglas Bridges |
| title_short | Constructive analysis |
| title_sort | constructive analysis |
| topic | Analyse (wiskunde) gtt Analyse mathématique - Fondements Constructieve wiskunde gtt Grondslagen gtt Mathematical analysis Foundations Konstruktive Analysis (DE-588)4473957-6 gnd |
| topic_facet | Analyse (wiskunde) Analyse mathématique - Fondements Constructieve wiskunde Grondslagen Mathematical analysis Foundations Konstruktive Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006128465&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT bishoperrett constructiveanalysis AT bridgesdouglass constructiveanalysis |