Topology: a geometric account of general topology, homotopy types and the fundamental groupoid
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| Previous Title: | Brown, Ronald Elements of modern topology |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Chichester u.a.
Ellis Horwood u.a.
1988
|
| Edition: | Rev., updated and expanded version |
| Series: | Ellis Horwood series in mathematics and its applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Früher u.d.T.: Brown, Ronald: Elements of modern topology. - Literaturverz. S.: 427 - 441 |
| Physical Description: | XVII, 460 S. zahlr. graph. Darst. |
| ISBN: | 0745802311 0470212179 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface to the first edition v
Preface to the second edition xii
1 Some topology on the real line 1
1.1 Neighbourhoods in R 1
1.2 Continuity 4
1.3 Open sets, closed sets, closure 9
1.4 Some generalizations 14
2 Topological spaces 17
2.1 Axioms for neighbourhoods 17
2.2 Open sets 20
2.3 Product spaces 24
2.4 Relative topologies and subspaces 28
2.5 Continuity 31
2.6 Other conditions for continuity 35
2.7 Comparison of topologies, homeomorphism 38
2.8 Metric spaces and normed vector spaces 42
2.9 Distance from a subset » 53
2.10 Hausdorff spaces 55
3 Connected spaces, compact spaces 61
3.1 The sum of topological spaces 61
3.2 Connected spaces 64
3.3 Components and locally connected spaces 67
3.4 Path connectedness 73
3.5 Compactness 77
V
vi TOPOLOGY
3.6 Further properties of compactness 84
Locally compact Spaces, normal Spaces 84
Proper maps 85
Lebesgue covering lemma 86
Compactifications 87
4 Identification Spaces and cell complexes 92
4.1 Introduction 92
4.2 Final topologies, identification topologies 95
4.3 Subspaces, products, and identification maps 100
4.4 Cells and spheres 107
4.5 Adjunction Spaces 112
4.6 Properties of adjunction Spaces 119
4.7 Cell complexes 124
5 Projective and other spaces 133
5.1 Quaternions 133
5.2 Normed vector Spaces again 137
5.3 Projective Spaces 139
5.4 Isometries of inner product Spaces 144
5.5 Simplicial complexes 149
5.6 Bases and sub bases for open sets; initial topologies 153
5.7 Joins 159
5.8 Smash products 167
5.9 The compact open topology 171
6 The fundamental groupoid 190
6.1 Categories 190
6.2 Construction of the fundamental groupoid 195
6.3 Properties of groupoids 203
6.4 Functors and morphisms of groupoids 206
6.5 Homotopies 212
6.6 Coproducts and pushouts 220
6.7 The fundamental groupoid of a union of spaces 226
7 Cofibrations 238
7.1 The track groupoid 239
7.2 Fibrations of groupoids 247
7.3 Examples 261
7.4 The gluing theorem for homotopy equivalences of
closed unions 267
CONTENTS vii
7.5 The homotopy type of adjunction Spaces 273
7.6 The cellular approximation theorem 286
8 Computation of the fundamental groupoid 293
8.1 Universal morphisms 293
8.2 Free groupoids 303
8.3 Quotient groupoids 308
8.4 The Van Kampen theorem 312
8.5 The Jordan curve theorem 326
9 Covering Spaces 334
9.1 Covering maps and covering homotopies 334
9.2 Covering groupoids 339
9.3 On lifting sums and morphisms 343
9.4 Existence of covering groupoids 347
9.5 Lifted topologies 352
9.6 The equivalence of categories 360
9.7 Induced coverings and pullbacks 367
9.8 Applications to subgroup theorems in group theory 372
9.9 Orbit Spaces and orbit groupoids 379
9.10 The computation of orbit groupoids: quotients and
semidirect products 388
Appendix: Functions and cardinality 402
A.l Functions 402
A.2 Finite, countable, and uncountable sets 406
A.3 Products and the axiom of choice 413
A.4 Universal constructions 415
Glossary of terms from set theory 422
References 427
Glossary of Symbols 442
Index 448
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| dewey-search | 514 |
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| discipline | Mathematik |
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| id | DE-604.BV001774009 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:35:47Z |
| institution | BVB |
| isbn | 0745802311 0470212179 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001195537 |
| oclc_num | 18520483 |
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| physical | XVII, 460 S. zahlr. graph. Darst. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Ellis Horwood u.a. |
| record_format | marc |
| series2 | Ellis Horwood series in mathematics and its applications |
| spelling | Brown, Ronald Verfasser aut Topology a geometric account of general topology, homotopy types and the fundamental groupoid Rev., updated and expanded version Chichester u.a. Ellis Horwood u.a. 1988 XVII, 460 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ellis Horwood series in mathematics and its applications Früher u.d.T.: Brown, Ronald: Elements of modern topology. - Literaturverz. S.: 427 - 441 Topologia larpcal Topologie ram Topology Topologie (DE-588)4060425-1 gnd rswk-swf Topologie (DE-588)4060425-1 s DE-604 Früher u.d.T. Brown, Ronald Elements of modern topology HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001195537&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brown, Ronald Topology a geometric account of general topology, homotopy types and the fundamental groupoid Topologia larpcal Topologie ram Topology Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 |
| title | Topology a geometric account of general topology, homotopy types and the fundamental groupoid |
| title_auth | Topology a geometric account of general topology, homotopy types and the fundamental groupoid |
| title_exact_search | Topology a geometric account of general topology, homotopy types and the fundamental groupoid |
| title_full | Topology a geometric account of general topology, homotopy types and the fundamental groupoid |
| title_fullStr | Topology a geometric account of general topology, homotopy types and the fundamental groupoid |
| title_full_unstemmed | Topology a geometric account of general topology, homotopy types and the fundamental groupoid |
| title_old | Brown, Ronald Elements of modern topology |
| title_short | Topology |
| title_sort | topology a geometric account of general topology homotopy types and the fundamental groupoid |
| title_sub | a geometric account of general topology, homotopy types and the fundamental groupoid |
| topic | Topologia larpcal Topologie ram Topology Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topologia Topologie Topology |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001195537&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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