Topology and groupoids:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Deganwy
BookSurge
2006
|
| Ausgabe: | Rev., updated, and expanded version |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Frühere Ausg. u.d.T.: Brown, Ronald: Elements of modern topology |
| Beschreibung: | XXVI, 512 S. graph. Darst. |
| ISBN: | 1419627228 |
Internformat
MARC
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| 010 | |a 006901092 | ||
| 020 | |a 1419627228 |c pbk. |9 1-419-62722-8 | ||
| 035 | |a (OCoLC)633053501 | ||
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| 100 | 1 | |a Brown, Ronald |d 1935- |e Verfasser |0 (DE-588)1018109226 |4 aut | |
| 245 | 1 | 0 | |a Topology and groupoids |c Ronald Brown |
| 250 | |a Rev., updated, and expanded version | ||
| 264 | 1 | |a Deganwy |b BookSurge |c 2006 | |
| 300 | |a XXVI, 512 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Frühere Ausg. u.d.T.: Brown, Ronald: Elements of modern topology | ||
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| 653 | 0 | |a Topologie | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016466564 | ||
Datensatz im Suchindex
| _version_ | 1804137600886243328 |
|---|---|
| adam_text | Contents
Preface
to the first edition
vii
Preface to the second edition
χ
Preface to the third edition
xviii
1
Some topology on the real line
1
1.1
Neighbourhoods in
К
...................... 1
1.2
Continuity
............................ 4
1.3
Open sets, closed sets, closure
................. 10
1.4
Some generalisations
...................... 15
2
Topological spaces
19
2.1
Axioms for neighbourhoods
.................. 20
2.2
Open sets
............................ 22
2.3
Product spaces
......................... 27
2.4
Relative topologies and subspaces
............... 30
2.5
Continuity
............................ 33
2.6
Other conditions for continuity
................ 38
2.7
Comparison of topologies, homeomorphism
......... 42
2.8
Metric spaces and normed vector spaces
........... 45
2.9
Distance from a subset
..................... 57
2.10
Hausdorff spaces
........................ 59
3
Connected spaces, compact spaces
65
3.1
The sum of topological spaces
................. 65
3.2
Connected spaces
........................ 68
3.3
Components and locally connected spaces
.......... 72
3.4
Path-connectedness
....................... 77
3.5
Compactness
.......................... 82
3.6
Further properties of compactness
.............. 89
4
Identification spaces and cell complexes
97
4.1
Introduction
........................... 97
4.2
Final topologies, identification topologies
.......... 101
4.3
Subspaces, products, and identification maps
........ 105
4.4
Cells and spheres
........................ 113
4.5
Adjunction spaces
........................ 118
4.6
Properties of adjunction spaces
................ 126
4.7
Cell complexes
......................... 131
5
Projective
and other spaces
141
5.1
Quaternions
........................... 141
5.2
Normed vector spaces again
.................. 146
5.3
Projective
spaces
........................ 147
5.4
Isometries of inner product spaces
.............. 152
5.5
Simplicial complexes
...................... 158
5.6
Bases and sub-bases for open sets; initial topologies
..... 162
5.7
Joins
............................... 168
5.8
The smash product
....................... 177
5.9
Spaces of functions, and the compact-open topology
.... 181
6
The fundamental groupoid
201
6.1
Categories
............................ 202
6.2
Construction of the fundamental groupoid
.......... 207
6.3
Properties of groupoids
..................... 215
6.4
Functors and morphisms of groupoids
............ 219
6.5
Homotopies
........................... 225
6.6
Coproducts and pushouts
................... 234
6.7
The fundamental groupoid of a union of spaces
....... 240
7
Cofibrations
253
7.1
The track groupoid
....................... 254
7.2
Fibrations of groupoids
..................... 262
7.3
Examples
............................ 277
7.4
The gluing theorem for homotopy equivalences of closed
unions
.............................. 283
7.5
The homotopy type of adjunction spaces
........... 290
7.6
The cellular approximation theorem
............. 303
8
Some combinatorial groupoid theory
311
8.1
Universal morphisms
...................... 312
8.2
Free groupoids
......................... 323
8.3
Quotient groupoids
....................... 329
8.4
Some computations
....................... 332
9
Computation of the fundamental groupoid
339
9.1
The Van
Kampen
theorem for adjunction spaces
....... 339
9.2
The Jordan Curve Theorem
.................. 352
10
Covering spaces, covering groupoids
359
10.1
Covering maps and covering homotopies
........... 360
10.2
Covering groupoids
....................... 365
10.3
On lifting sums and morphisms
................ 369
10.4
Existence
of covering groupoids
................ 373
10.5
Lifted topologies
........................ 379
10.6
The equivalence of categories
................. 387
10.7
Induced coverings and pullbacks
............... 393
10.8
Applications to subgroup theorems in group theory
..... 399
11
Orbit spaces, orbit groupoids
409
11.1
Groups acting on spaces
.................... 409
11.2
Groups acting on groupoids
.................. 415
11.3
General normal subgroupoids and quotient groupoids
. . . . 419
11.4
The semidirect product groupoid
............... 424
11.5
Semidirect product and orbit groupoids
........... 426
11.6
Full subgroupoids of orbit groupoids
............. 431
12
Conclusion
437
A Functions, cardinality, universal properties
443
A.1 Functions
............................ 443
A.2 Finite, countable and uncountable sets
............ 448
A.3 Products and the axiom of choice
............... 454
A.4 Universal properties
...................... 457
Glossary of terms from set theory
465
Bibliography
470
Glossary of symbols
493
Index
499
|
| adam_txt |
Contents
Preface
to the first edition
vii
Preface to the second edition
χ
Preface to the third edition
xviii
1
Some topology on the real line
1
1.1
Neighbourhoods in
К
. 1
1.2
Continuity
. 4
1.3
Open sets, closed sets, closure
. 10
1.4
Some generalisations
. 15
2
Topological spaces
19
2.1
Axioms for neighbourhoods
. 20
2.2
Open sets
. 22
2.3
Product spaces
. 27
2.4
Relative topologies and subspaces
. 30
2.5
Continuity
. 33
2.6
Other conditions for continuity
. 38
2.7
Comparison of topologies, homeomorphism
. 42
2.8
Metric spaces and normed vector spaces
. 45
2.9
Distance from a subset
. 57
2.10
Hausdorff spaces
. 59
3
Connected spaces, compact spaces
65
3.1
The sum of topological spaces
. 65
3.2
Connected spaces
. 68
3.3
Components and locally connected spaces
. 72
3.4
Path-connectedness
. 77
3.5
Compactness
. 82
3.6
Further properties of compactness
. 89
4
Identification spaces and cell complexes
97
4.1
Introduction
. 97
4.2
Final topologies, identification topologies
. 101
4.3
Subspaces, products, and identification maps
. 105
4.4
Cells and spheres
. 113
4.5
Adjunction spaces
. 118
4.6
Properties of adjunction spaces
. 126
4.7
Cell complexes
. 131
5
Projective
and other spaces
141
5.1
Quaternions
. 141
5.2
Normed vector spaces again
. 146
5.3
Projective
spaces
. 147
5.4
Isometries of inner product spaces
. 152
5.5
Simplicial complexes
. 158
5.6
Bases and sub-bases for open sets; initial topologies
. 162
5.7
Joins
. 168
5.8
The smash product
. 177
5.9
Spaces of functions, and the compact-open topology
. 181
6
The fundamental groupoid
201
6.1
Categories
. 202
6.2
Construction of the fundamental groupoid
. 207
6.3
Properties of groupoids
. 215
6.4
Functors and morphisms of groupoids
. 219
6.5
Homotopies
. 225
6.6
Coproducts and pushouts
. 234
6.7
The fundamental groupoid of a union of spaces
. 240
7
Cofibrations
253
7.1
The track groupoid
. 254
7.2
Fibrations of groupoids
. 262
7.3
Examples
. 277
7.4
The gluing theorem for homotopy equivalences of closed
unions
. 283
7.5
The homotopy type of adjunction spaces
. 290
7.6
The cellular approximation theorem
. 303
8
Some combinatorial groupoid theory
311
8.1
Universal morphisms
. 312
8.2
Free groupoids
. 323
8.3
Quotient groupoids
. 329
8.4
Some computations
. 332
9
Computation of the fundamental groupoid
339
9.1
The Van
Kampen
theorem for adjunction spaces
. 339
9.2
The Jordan Curve Theorem
. 352
10
Covering spaces, covering groupoids
359
10.1
Covering maps and covering homotopies
. 360
10.2
Covering groupoids
. 365
10.3
On lifting sums and morphisms
. 369
10.4
Existence
of covering groupoids
. 373
10.5
Lifted topologies
. 379
10.6
The equivalence of categories
. 387
10.7
Induced coverings and pullbacks
. 393
10.8
Applications to subgroup theorems in group theory
. 399
11
Orbit spaces, orbit groupoids
409
11.1
Groups acting on spaces
. 409
11.2
Groups acting on groupoids
. 415
11.3
General normal subgroupoids and quotient groupoids
. . . . 419
11.4
The semidirect product groupoid
. 424
11.5
Semidirect product and orbit groupoids
. 426
11.6
Full subgroupoids of orbit groupoids
. 431
12
Conclusion
437
A Functions, cardinality, universal properties
443
A.1 Functions
. 443
A.2 Finite, countable and uncountable sets
. 448
A.3 Products and the axiom of choice
. 454
A.4 Universal properties
. 457
Glossary of terms from set theory
465
Bibliography
470
Glossary of symbols
493
Index
499 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Brown, Ronald 1935- |
| author_GND | (DE-588)1018109226 |
| author_facet | Brown, Ronald 1935- |
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| building | Verbundindex |
| bvnumber | BV023281771 |
| classification_rvk | SK 280 |
| ctrlnum | (OCoLC)633053501 (DE-599)HBZHT014977468 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Rev., updated, and expanded version |
| format | Book |
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| id | DE-604.BV023281771 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:39:59Z |
| indexdate | 2024-07-09T21:14:53Z |
| institution | BVB |
| isbn | 1419627228 |
| language | English |
| lccn | 006901092 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016466564 |
| oclc_num | 633053501 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-384 DE-703 DE-20 |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-703 DE-20 |
| physical | XXVI, 512 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | BookSurge |
| record_format | marc |
| spelling | Brown, Ronald 1935- Verfasser (DE-588)1018109226 aut Topology and groupoids Ronald Brown Rev., updated, and expanded version Deganwy BookSurge 2006 XXVI, 512 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Frühere Ausg. u.d.T.: Brown, Ronald: Elements of modern topology Topologie (DE-588)4060425-1 gnd rswk-swf Gruppoid (DE-588)4158484-3 gnd rswk-swf Topologie Topologie (DE-588)4060425-1 s Gruppoid (DE-588)4158484-3 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016466564&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brown, Ronald 1935- Topology and groupoids Topologie (DE-588)4060425-1 gnd Gruppoid (DE-588)4158484-3 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4158484-3 |
| title | Topology and groupoids |
| title_auth | Topology and groupoids |
| title_exact_search | Topology and groupoids |
| title_exact_search_txtP | Topology and groupoids |
| title_full | Topology and groupoids Ronald Brown |
| title_fullStr | Topology and groupoids Ronald Brown |
| title_full_unstemmed | Topology and groupoids Ronald Brown |
| title_short | Topology and groupoids |
| title_sort | topology and groupoids |
| topic | Topologie (DE-588)4060425-1 gnd Gruppoid (DE-588)4158484-3 gnd |
| topic_facet | Topologie Gruppoid |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016466564&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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