An introduction to topology and homotopy:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston
PWS-Kent Publ.
1992
|
| Series: | The Prindle, Weber & Schmidt series in advanced mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 466 - 467 |
| Physical Description: | XIII, 479 S. graph. Darst. |
| ISBN: | 0534929605 |
Staff View
MARC
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| 245 | 1 | 0 | |a An introduction to topology and homotopy |c Allan J. Sieradski |
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| 300 | |a XIII, 479 S. |b graph. Darst. | ||
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| 490 | 0 | |a The Prindle, Weber & Schmidt series in advanced mathematics | |
| 500 | |a Literaturverz. S. 466 - 467 | ||
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| 650 | 4 | |a Homotopy theory | |
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Record in the Search Index
| _version_ | 1804120376938070016 |
|---|---|
| adam_text | CONTENTS
PART ONE: TOPOLOGY l
Chapter 1 Preliminaries 3
1 The Topological Viewpoint 3
2 Set Theory 8
3 The Real Line 16
4 Functions 21
5 Relations 28
Exercises, Sections 1 5 36
Chapter 2 Metric Topology 42
1 Topology of the Euclidean Line 42
2 Topology of Euclidean Space 49
3 Metric Topology 54
4 Continuous Functions 63
5 Completeness 68
Exercises, Sections 1 5 75
Chapter 3 Metric Space Properties 85
1 Connected Spaces 85
2 Sequentially Compact Metric Spaces 89
3 Hyperspace of Compact Subspaces 96
4 Topological Equivalence 101
5 Peano s Curve 105
Exercises, Sections 1 5 109
Chapter 4 Topological Spaces 116
1 Topologies 116
2 Topological Separation 122
3 Interior, Closure, and Boundary 127
4 Continuous Functions 131
Exercises, Sections 1 4 136
xi
Xii CONTENTS
Chapter 5 Construction of Spaces 143
1 Subspaces and Identification Spaces 143
2 Topological Bases 151
3 Topological Unions and Products 156
4 Weak Topologies and Adjunction Spaces 163
Exercises, Sections 1 4 168
Chapter 6 Connectedness 175
1 Connected Spaces 175
2 Components 180
3 Path Connectedness 186
Exercises, Sections 1 3 192
Chapter 7 Compactness 197
1 Compact Spaces 197
2 Topological Aspects of Compactness 201
3 Compactness in Metric Spaces 207
4 Locally Compact Spaces 211
5 A Characterization of Arcs 218
Exercises, Sections 1 5 226
Chapter 8 Separation and Covering Properties 233
1 Normal Spaces 233
2 Completely Regular Spaces 241
3 Metrization Theorems 247
4 Paracompact Spaces 254
Exercises, Sections 1 5 259
PART TWO: HOMOTOPY 263
Chapter 9 Fundamental Group 265
1 The Fundamental Groupoid 265
2 Path Homotopy in Spheres 272
3 The Fundamental Group 280
4 Poincare Index Formula 285
Exercises, Sections 1 4 292
Chapter 10 Homotopy 296
1 Categories and Functors 296
2 Basic Homotopy Concepts 301
3 Homotopy Category 305
4 Fibrations and Cofibrations 312
5 Homotopy Equivalences 317
Exercises, Sections 1 5 323
CONTENTS Xiii
Chapter 11 Group Theory 328
1 Overview 328
2 Groups and Homomorphisms 331
3 Products and Sums of Groups 335
4 Quotient Groups 340
Exercises, Sections 2 4 347
Chapter 12 Calculations of Kj 350
1 The Seifert Van Kampen Theorem 350
2 Polygonal Complexes 357
3 Knot Theory 364
Exercises, Sections 1 3 372
Chapter 13 Surfaces 374
1 Polygonal Surfaces 374
2 Classification of Surfaces 379
3 Euler Characteristic 385
4 Poincare s Index Theorem 390
Exercises, Sections 1 4 394
Chapter 14 Covering Spaces 399
1 Fundamentals 399
2 Liftings of Paths and Homotopies 403
3 General Liftings 409
4 Fundamental Theorem 413
5 Intermediate Covering Spaces 418
6 Group Actions and Geometries 425
Exercises, Sections 1 6 430
Chapter 15 CW Complexes 435
1 Cell Complexes 435
2 Fundamental Group of a CW Complex 444
3 Covering Spaces of CW Complexes 454
Exercises, Sections 1 3 462
Bibliography 466
Index 468
|
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| discipline | Mathematik |
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| id | DE-604.BV006149300 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:41:07Z |
| institution | BVB |
| isbn | 0534929605 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003888420 |
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| physical | XIII, 479 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | PWS-Kent Publ. |
| record_format | marc |
| series2 | The Prindle, Weber & Schmidt series in advanced mathematics |
| spelling | Sieradski, Allan J. Verfasser aut An introduction to topology and homotopy Allan J. Sieradski Boston PWS-Kent Publ. 1992 XIII, 479 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Prindle, Weber & Schmidt series in advanced mathematics Literaturverz. S. 466 - 467 Homotopie ram Topologie ram Homotopy theory Topology HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003888420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sieradski, Allan J. An introduction to topology and homotopy Homotopie ram Topologie ram Homotopy theory Topology |
| title | An introduction to topology and homotopy |
| title_auth | An introduction to topology and homotopy |
| title_exact_search | An introduction to topology and homotopy |
| title_full | An introduction to topology and homotopy Allan J. Sieradski |
| title_fullStr | An introduction to topology and homotopy Allan J. Sieradski |
| title_full_unstemmed | An introduction to topology and homotopy Allan J. Sieradski |
| title_short | An introduction to topology and homotopy |
| title_sort | an introduction to topology and homotopy |
| topic | Homotopie ram Topologie ram Homotopy theory Topology |
| topic_facet | Homotopie Topologie Homotopy theory Topology |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003888420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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