A geometric introduction to topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass.
Addison-Wesley
1972
|
| Series: | Addison-Wesley series in mathematics.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 168 S. Ill., graph. Darst. |
Staff View
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| 245 | 1 | 0 | |a A geometric introduction to topology |c C. T. C. Wall |
| 264 | 1 | |a Reading, Mass. |b Addison-Wesley |c 1972 | |
| 300 | |a VI, 168 S. |b Ill., graph. Darst. | ||
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| 490 | 0 | |a Addison-Wesley series in mathematics. | |
| 650 | 7 | |a Homotopia |2 larpcal | |
| 650 | 7 | |a Topologia |2 larpcal | |
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Record in the Search Index
| _version_ | 1804117306088882176 |
|---|---|
| adam_text | CONTENTS
PART 0 PRELIMINARIES
Chapter 0 Notations and Prerequisites
Numbers 1 ? Sets and maps 1 ? Equivalence relations 3
Chapter 1 Spaces and Continuous Maps
Introduction 5 ? Continuity 5 ? Homeomorphism 7 ?
Neighborhoods, open and closed sets 11 ? Compactness 15
Chapter 2 Abelian Groups
Introduction 21 ? Definitions 21 ? Direct sums 23 ? Exact
sequences 27 Q Free abelian groups 31
PART 1 INTRODUCTION TO HOMOTOPY THEORY
Chapter 3 Connected and Disconnected Spaces
Introduction 41 ? Connectedness 41 ? Path connectedness 43 ?
Local path connectedness 45
Chapter 4 More about Connection
Introduction 49 D The group H°(X) 49 ? The set no(X) 50D
The group H0(X) 53
Chapter 5 Definition of Homotopy
Introduction 57 ? Definition of homotopy 57 ? Homotopy
equivalence 60 ? Homotopy sets; the groups H^X) 61
Chapter 6 A Study of a Circle
Introduction 65 ? Lifting maps from S1 up to R 65 ? The degree of a
map 68 ? Applications 70
Chapter 7 Lifting and Extension Problems
Introduction 74 ? The lifting problem 75 ? The extension problem 79
Chapter 8 Calculations
Introduction 84 ? The Mayer Vietoris theorem 84 D First calculations
87 D Graphs 90 ? Products 91
v
vi Contents
PART 2 THE DUALITY THEOREM
Chapter 9 Eilenberg s Separation Criterion
Introduction 99 ? Complementary components 99 ? Separation of
points by compact plane sets 100
Chapter 10 The Duality Map
Introduction 104 ? Construction of the duality map 104 ?
Proof of injectivity 106
Chapter 11 Proof of the Duality Theorem
Introduction 111 ? An extension theorem 113 ? Naturality 116 ?
Proof in some special cases 116 Q End of the proof 119
Chapter 12 Remarks on the Proof
Introduction 122 ? The extended plane 122 ? Reformulation of
preceding chapters 124 ? The Hopf map 125
PART 3 FURTHER RESULTS IN THE TOPOLOGY OF PLANE SETS
Chapter 13 The Jordan Curve Theorem
Introduction 133 ? Theta curves 133 ? First alternative proof (after
Dieudonne) 135 D Point sets in R and S 137 ? Second alternative
proof (after Doyle) 139 D Invariance of (plane) domains 140
Chapter 14 Further Duality Properties
Introduction 143 ? The group H^X) 143 D Properties ofH^X) 146 D
Duality 147 ? Plane domains 148
Chapter 15 Geometric Integration Theory
Introduction 153 ? Line integrals in R2 153 D Green s theorem 154 ?
Reformulation in terms of homology 157 ? The three dimensional
case 160 D The complex case 162
Index of Terms
165
Index of Notation
168
|
| any_adam_object | 1 |
| author | Wall, C. T. C. 1936- |
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| author_role | aut |
| author_sort | Wall, C. T. C. 1936- |
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| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612 |
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| callnumber-sort | QA 3612 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 280 SK 350 |
| ctrlnum | (OCoLC)375528 (DE-599)BVBBV003017300 |
| dewey-full | 514/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.2 |
| dewey-search | 514/.2 |
| dewey-sort | 3514 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:52:18Z |
| institution | BVB |
| language | English |
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| physical | VI, 168 S. Ill., graph. Darst. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Addison-Wesley |
| record_format | marc |
| series2 | Addison-Wesley series in mathematics. |
| spelling | Wall, C. T. C. 1936- Verfasser (DE-588)107575256 aut A geometric introduction to topology C. T. C. Wall Reading, Mass. Addison-Wesley 1972 VI, 168 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics. Homotopia larpcal Topologia larpcal Topologie algébrique Algebraic topology Geometrie (DE-588)4020236-7 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Topologie (DE-588)4060425-1 s DE-604 Geometrie (DE-588)4020236-7 s Algebraische Topologie (DE-588)4120861-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001888968&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wall, C. T. C. 1936- A geometric introduction to topology Homotopia larpcal Topologia larpcal Topologie algébrique Algebraic topology Geometrie (DE-588)4020236-7 gnd Algebraische Topologie (DE-588)4120861-4 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4120861-4 (DE-588)4060425-1 (DE-588)4151278-9 |
| title | A geometric introduction to topology |
| title_auth | A geometric introduction to topology |
| title_exact_search | A geometric introduction to topology |
| title_full | A geometric introduction to topology C. T. C. Wall |
| title_fullStr | A geometric introduction to topology C. T. C. Wall |
| title_full_unstemmed | A geometric introduction to topology C. T. C. Wall |
| title_short | A geometric introduction to topology |
| title_sort | a geometric introduction to topology |
| topic | Homotopia larpcal Topologia larpcal Topologie algébrique Algebraic topology Geometrie (DE-588)4020236-7 gnd Algebraische Topologie (DE-588)4120861-4 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Homotopia Topologia Topologie algébrique Algebraic topology Geometrie Algebraische Topologie Topologie Einführung |
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