Basic topology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1997
|
| Ausgabe: | Corr. 5. print. |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 251 S. graph. Darst. |
| ISBN: | 3540908390 |
Internformat
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Datensatz im Suchindex
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| adam_text | *. *. ARMSTRONG BASIC TOPOLOGY WITH 132 ILLUSTRATIONS SPRINGER CONTENTS
PREFACE VII CHAPTER 1 INTRODUCTION 1. EULER S THEOREM 1 2. TOPOLOGICAL
EQUIVALENCE 4 3. SURFACES 8 4. ABSTRACT SPACES 12 5. A CLASSIFICATION
THEOREM 16 6. TOPOLOGICAL INVARIANTS 19 CHAPTER 2 CONTINUITY 1. OPEN AND
CLOSED SETS 27 2. CONTINUOUS FUNCTIONS 32 3. A SPACE-FILLING CURVE 36 4.
THE TIETZE EXTENSION THEOREM 38 CHAPTER 3 COMPACTNESS AND CONNECTEDNESS
1. CLOSED BOUNDED SUBSETS OF E 43 2. THE HEINE-BOREL THEOREM 44 3.
PROPERTIES OF COMPACT SPACES 47 4. PRODUCT SPACES 51 5. CONNECTEDNESS 56
6. JOINING POINTS BY PATHS 61 CHAPTER 4 IDENTIFICATION SPACES 1.
CONSTRUCTING A MOEBIUS STRIP 65 2. THE IDENTIFICATION TOPOLOGY 66 3.
TOPOLOGICAL GROUPS 73 4. ORBIT SPACES 78 CHAPTER 5 THE FUNDAMENTAL GROUP
1. HOMOTOPIC MAPS 87 2. CONSTRUCTION OF THE FUNDAMENTAL GROUP 92 3.
CALCULATIONS 96 4. HOMOTOPY TYPE 103 5. THE BROUWER FIXED-POINT THEOREM
110 6. SEPARATION OF THE PLANE 112 7. THE BOUNDARY OF A SURFACE 115 XI
CONTENTS CHAPTER 6 TRIANGULATIONS 1. TRIANGULATING SPACES 119 2.
BARYCENTRIC SUBDIVISION 125 3. SIMPLICIAL APPROXIMATION 127 4. THE EDGE
GROUP OF A COMPLEX 131 5. TRIANGULATING ORBIT SPACES 140 6. INFINITE
COMPLEXES 143 CHAPTER 7 SURFACES 1. CLASSIFICATION 149 2. TRIANGULATION
AND ORIENTATION 153 3. EULER CHARACTERISTICS 158 4. SURGERY 161 5.
SURFACE SYMBOLS 165 CHAPTER 8 SIMPLICIAL HOMOLOGY 1. CYCLES AND
BOUNDARIES 173 2. HOMOLOGY GROUPS 176 3. EXAMPLES 179 4. SIMPLICIAL MAPS
184 5. STELLAR SUBDIVISION 185 6. INVARIANCE 188 CHAPTER 9 DEGREE AND
LEFSCHETZ NUMBER 1. MAPS OF SPHERES 195 2. THE EULER-POINCARE FORMULA
199 3. THE BORSUK-ULAM THEOREM 202 4. THE LEFSCHETZ FIXED-POINT THEOREM
206 5. DIMENSION 210 CHAPTER 10 KNOTS AND COVERING SPACES 1. EXAMPLES OF
KNOTS 213 2. THE KNOT GROUP 216 3. SEIFERT SURFACES 223 4. COVERING
SPACES 227 5. THE ALEXANDER POLYNOMIAL 234 APPENDIX: GENERATORS AND
RELATIONS 241 BIBLIOGRAPHY 244 INDEX 246 XII
|
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| bvnumber | BV023769011 |
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| discipline | Mathematik |
| edition | Corr. 5. print. |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV023769011 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:36:25Z |
| institution | BVB |
| isbn | 3540908390 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017411249 |
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| physical | XII, 251 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Armstrong, Mark A. Verfasser (DE-588)110755316 aut Basic topology M. A. Armstrong Corr. 5. print. New York [u.a.] Springer 1997 XII, 251 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Topologie (DE-588)4060425-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Topologie (DE-588)4060425-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017411249&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Armstrong, Mark A. Basic topology Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4151278-9 |
| title | Basic topology |
| title_auth | Basic topology |
| title_exact_search | Basic topology |
| title_full | Basic topology M. A. Armstrong |
| title_fullStr | Basic topology M. A. Armstrong |
| title_full_unstemmed | Basic topology M. A. Armstrong |
| title_short | Basic topology |
| title_sort | basic topology |
| topic | Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topologie Einführung |
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