Topology of surfaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1993
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 262 S. Ill., graph. Darst. |
| ISBN: | 0387941029 3540941029 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1823026249370435584 |
|---|---|
| adam_text |
L. CHRISTINE KINSEY
TOPOLOGY
OF
SURFACES
WITH 276 ILLUSTRATIONS
SPRINGER-VERLAG
NEW
YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO
HONGKONG BARCELONA BUDAPEST
CONTENTS
PREFACE V
CHAPTER 1. INTRODUCTION TO TOPOLOGY 1
1.1. AN OVERVIEW 1
CHAPTER 2. POINT-SET TOPOLOGY IN R
N
7
2.1.
OPEN AND CLOSED SETS IN R
N
7
2.2.
RELATIVE NEIGHBORHOODS 16
2.3.
CONTINUITY 19
2.4. COMPACT SETS 26
2.5.
CONNECTED SETS 29
2.6.
APPLICATIONS 31
CHAPTER 3. POINT-SET TOPOLOGY 36
3.1.
OPEN SETS AND NEIGHBORHOODS 36
3.2. CONTINUITY, CONNECTEDNESS, AND COMPACTNESS 42
3.3.
SEPARATION AXIOMS 46
3.4. PRODUCT SPACES 47
3.5.
QUOTIENT SPACES 51
CHAPTER 4. SURFACES 55
4.1.
COMPLEXES 55
4.2.
SURFACES 64
4.3.
TRIANGULATIONS 73
4.4.
CLASSIFICATION OF SURFACES 79
4.5.
SURFACES WITH BOUNDARY 86
CHAPTER 5. THE EULER CHARACTERISTIC 90
5.1.
TOPOLOGICAL INVARIANTS 90
5.2. GRAPHS AND TREES 91
5.3.
THE EULER CHARACTERISTIC AND THE SPHERE 97
5.4. THE EULER CHARACTERISTIC AND SURFACES 104
5.5.
MAP-COLORING PROBLEMS 109
VIII CONTENTS
CHAPTER 6. HOMOLOGY
6.1.
THE ALGEBRA OF CHAINS
6.2.
HOMOLOGY
6.3.
MORE COMPUTATIONS
6.4.
BETTI NUMBERS AND THE EULER CHARACTERISTIC
CHAPTER 7. CELLULAR FUNCTIONS
7.1.
CELLULAR FUNCTIONS
7.2.
HOMOLOGY AND CELLULAR FUNCTIONS
7.3.
EXAMPLES
7.4.
COVERING SPACES
CHAPTER 8. INVARIANCE OF HOMOLOGY
8.1.
INVARIANCE OF HOMOLOGY FOR SURFACES
8.2.
THE SIMPLICIAL APPROXIMATION THEOREM
CHAPTER 9. HOMOTOPY
9.1.
HOMOTOPY AND HOMOLOGY
9.2.
THE FUNDAMENTAL GROUP
CHAPTER 10. MISCELLANY
10.1.
APPLICATIONS
10.2.
THE JORDAN CURVE THEOREM
10.3.
3-MANIFOLDS
CHAPTER 11. TOPOLOGY AND CALCULUS
11.1.
VECTOR FIELDS AND DIFFERENTIAL EQUATIONS IN
11.2.
DIFFERENTIABLE MANIFOLDS
11.3.
VECTOR FIELDS ON MANIFOLDS
11.4.
INTEGRATION ON MANIFOLDS
APPENDIX: GROUPS
REFERENCES
INDEX |
| any_adam_object | 1 |
| author | Kinsey, Laura Christine |
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| bvnumber | BV009132607 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA611 |
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| classification_rvk | SK 280 SK 300 SK 350 |
| classification_tum | MAT 572f MAT 146f |
| ctrlnum | (OCoLC)246692402 (DE-599)BVBBV009132607 |
| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2025-02-03T09:01:49Z |
| institution | BVB |
| isbn | 0387941029 3540941029 |
| language | English |
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| physical | VIII, 262 S. Ill., graph. Darst. |
| publishDate | 1993 |
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| publisher | Springer |
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| series2 | Undergraduate texts in mathematics |
| spelling | Kinsey, Laura Christine Verfasser (DE-588)113682344 aut Topology of surfaces L. Christine Kinsey New York u.a. Springer 1993 VIII, 262 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Topology Oberfläche (DE-588)4042907-6 gnd rswk-swf Geometrische Topologie (DE-588)4156724-9 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Oberfläche (DE-588)4042907-6 s Topologie (DE-588)4060425-1 s DE-604 Geometrische Topologie (DE-588)4156724-9 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006053167&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kinsey, Laura Christine Topology of surfaces Topology Oberfläche (DE-588)4042907-6 gnd Geometrische Topologie (DE-588)4156724-9 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4042907-6 (DE-588)4156724-9 (DE-588)4060425-1 |
| title | Topology of surfaces |
| title_auth | Topology of surfaces |
| title_exact_search | Topology of surfaces |
| title_full | Topology of surfaces L. Christine Kinsey |
| title_fullStr | Topology of surfaces L. Christine Kinsey |
| title_full_unstemmed | Topology of surfaces L. Christine Kinsey |
| title_short | Topology of surfaces |
| title_sort | topology of surfaces |
| topic | Topology Oberfläche (DE-588)4042907-6 gnd Geometrische Topologie (DE-588)4156724-9 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topology Oberfläche Geometrische Topologie Topologie |
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