Essential topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Springer
2005
|
| Series: | Springer undergraduate mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 224 S. Ill., graph. Darst. |
| ISBN: | 1852337826 9781852337827 |
Staff View
MARC
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| 100 | 1 | |a Crossley, Martin D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Essential topology |c Martin D. Crossley |
| 264 | 1 | |a London |b Springer |c 2005 | |
| 300 | |a IX, 224 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1804133529872760832 |
|---|---|
| adam_text | Contents
1.
Introduction
................................................ 1
2.
Continuous Functions
....................................... 3
2.1
Naïve
Continuity
......................................... 3
2.2
Rigorous Continuity
...................................... 5
2.3
Open Sets
............................................... 8
2.4
Continuity by Open Sets
.................................. 11
3.
Topological Spaces
.......................................... 15
3.1
Topological Spaces
........................................ 15
3.2
More Examples of Topological Spaces
....................... 19
3.3
Continuity in the Subspace Topology
....................... 28
3.4
Bases
................................................... 31
Interlude
....................................................... 35
4.
Topological Properties
...................................... 37
4.1
Connectivity
............................................. 37
4.2
Compactness
............................................. 43
4.3
The Hausdorff Property
................................... 50
5.
Deconstructionist Topology
................................. 55
5.1
Homeomorphisms
........................................ 55
5.2
Disjoint Unions
.......................................... 66
5.3
Product Spaces
.......................................... 71
5.4
Quotient Spaces
.......................................... 76
Interlude
....................................................... 89
6.
Homotopy
.................................................. 91
6.1
Homotopy
............................................... 91
6.2
Homotopy Equivalence
.................................... 96
6.3
The Circle
...............................................102
6.4
Brouwer s Fixed-Point Theorem
............................
ПО
6.5
Vector Fields
............................................112
7.
The
Euler
Number
.........................................117
7.1
Simplicial Complexes
.....................................117
7.2
The
Euler
Number
.......................................121
7.3
The
Euler
Characteristic and Surfaces
.......................124
8.
Homotopy Groups
..........................................127
8.1
Homotopy Groups
........................................128
8.2
Induced Homomorphisms
..................................136
8.3
The Fundamental Group
..................................140
8.4
Path Connectivity and
πο
.................................141
8.5
The Van
Kampen
Theorem
................................144
9.
Simplicial Homology
........................................149
9.1
Simplicial Homology Modulo
2.............................150
9.2
Limitations of Homology Modulo
2.........................158
9.3
Integral Simplicial Homology
...............................160
10.
Singular Homology
.........................................167
10.1
Singular Homology
.......................................167
10.2
Homology and Continuous Maps
...........................173
10.3
Homology Respects Homotopies
............................175
10.4
Barycentric Subdivision
................................... 180
10.5
The Mayer-Vietoris Sequence
..............................185
10.6
Homology and Homotopy Groups
...........................193
10.7
Comparison of Singular and Simplicial Homology
.............194
11.
More Deconstructionism
....................................197
11.1
Wedge Products
..........................................197
11.2
Suspensions and Loop Spaces
..............................199
11.3
Fibre Bundles
.............................................204
11.4
Vector Bundles
...........................................209
Solutions to Selected Exercises
.................................213
Contents ,
і)
Bibliography
....................................................21
Index
...........................................................21!
|
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| discipline | Mathematik |
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| id | DE-604.BV019986133 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:10:10Z |
| institution | BVB |
| isbn | 1852337826 9781852337827 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013308126 |
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| physical | IX, 224 S. Ill., graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer undergraduate mathematics series |
| spelling | Crossley, Martin D. Verfasser aut Essential topology Martin D. Crossley London Springer 2005 IX, 224 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Topology Textbooks Topologie (DE-588)4060425-1 gnd rswk-swf Topologie (DE-588)4060425-1 s DE-604 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013308126&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Crossley, Martin D. Essential topology Topology Textbooks Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 |
| title | Essential topology |
| title_auth | Essential topology |
| title_exact_search | Essential topology |
| title_full | Essential topology Martin D. Crossley |
| title_fullStr | Essential topology Martin D. Crossley |
| title_full_unstemmed | Essential topology Martin D. Crossley |
| title_short | Essential topology |
| title_sort | essential topology |
| topic | Topology Textbooks Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topology Textbooks Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013308126&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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