Elementary topology: problem textbook
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 400 S. Ill., graph. Darst. |
| ISBN: | 9780821845066 |
Internformat
MARC
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|---|---|---|---|
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| 245 | 1 | 0 | |a Elementary topology |b problem textbook |c O. Ya. Viro ... |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2008 | |
| 300 | |a XX, 400 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Topologie - Manuels d'enseignement supérieur | |
| 650 | 7 | |a Topologie - Problèmes et exercices |2 ram | |
| 650 | 4 | |a Topology |v Textbooks | |
| 650 | 0 | 7 | |a Topologie |0 (DE-588)4060425-1 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
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| 700 | 1 | |a Viro, Oleg Janovič |d 1948- |e Sonstige |0 (DE-588)1089145128 |4 oth | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016740663 | |
Datensatz im Suchindex
| _version_ | 1808860322367275008 |
|---|---|
| adam_text |
Contents
Introduction
xi
Part
1.
General
Topology
Chapter I. Structures and Spaces
3
1.
Set-Theoretic Digression: Sets
3
2.
Topology on a Set
11
3.
Bases
16
4.
Metric Spaces
18
5.
Subspaces
27
6.
Position of a Point with Respect to a Set
29
7.
Ordered Sets
35
8.
Cyclic Orders
42
Proofs and Comments
45
Chapter II. Continuity
55
9.
Set-Theoretic Digression: Maps
55
10.
Continuous Maps
59
11.
Homeomorphisms
67
Proofs and Comments
76
Chapter III. Topological Properties
83
12.
Connectedness
83
13.
Application of Connectedness
89
vu
VIU
Contents
14.
Path Connectedness
92
15.
Separation Axioms
97
16.
Countability Axioms
103
17.
Compactness
108
18.
Sequential Compactness
114
19x. Local Compactness and Paracompactness
117
Proofs and Comments
122
Chapter IV. Topological Constructions
135
20.
Multiplication
135
21.
Quotient Spaces
141
22.
Zoo of Quotient Spaces
145
23.
Projective
Spaces
155
24x. Finite Topological Spaces
159
25x. Spaces of Continuous Maps
163
Proofs and Comments
167
Chapter V. Topological Algebra
179
26x. Generalities on Groups
181
27x. Topological Groups
187
28x. Constructions
191
29x. Actions of Topological Groups
196
Proofs and Comments
200
Part
2.
Elements of Algebraic Topology
Chapter VI. Fundamental Group
207
30.
Homotopy
207
31.
Homotopy Properties of Path Multiplication
212
32.
Fundamental Group
215
33.
The Role of Base Point
220
Proofs and Comments
223
Chapter
VII.
Covering Spaces and Calculation of Fundamental Groups
231
34.
Covering Spaces
231
35.
Theorems on Path Lifting
235
36.
Calculation of Fundamental Groups by Using Universal
Coverings
237
Contents ix
Proofs and Comments
242
Chapter
VIII.
Fundamental Group and Maps
247
37.
Induced Homomorphisms
and Their First Applications
247
38.
Retractions and Fixed Points
253
39.
Homotopy Equivalences
256
40.
Covering Spaces via Fundamental Groups
261
41x. Classification of Covering Spaces
263
Proofs and Comments
269
Chapter IX. Cellular Techniques
279
42.
Cellular Spaces
279
43x. Topological Properties of Cellular Spaces
286
44.
Cellular Constructions
288
45.
One-Dimensional Cellular Spaces
291
46.
Fundamental Group of a Cellular Space
295
Proofs and Comments
304
Hints, Comments, Advices, Solutions, and Answers
317
Bibliography
393
Index
395 |
| adam_txt |
Contents
Introduction
xi
Part
1.
General
Topology
Chapter I. Structures and Spaces
3
1.
Set-Theoretic Digression: Sets
3
2.
Topology on a Set
11
3.
Bases
16
4.
Metric Spaces
18
5.
Subspaces
27
6.
Position of a Point with Respect to a Set
29
7.
Ordered Sets
35
8.
Cyclic Orders
42
Proofs and Comments
45
Chapter II. Continuity
55
9.
Set-Theoretic Digression: Maps
55
10.
Continuous Maps
59
11.
Homeomorphisms
67
Proofs and Comments
76
Chapter III. Topological Properties
83
12.
Connectedness
83
13.
Application of Connectedness
89
vu
VIU
Contents
14.
Path Connectedness
92
15.
Separation Axioms
97
16.
Countability Axioms
103
17.
Compactness
108
18.
Sequential Compactness
114
19x. Local Compactness and Paracompactness
117
Proofs and Comments
122
Chapter IV. Topological Constructions
135
20.
Multiplication
135
21.
Quotient Spaces
141
22.
Zoo of Quotient Spaces
145
23.
Projective
Spaces
155
24x. Finite Topological Spaces
159
25x. Spaces of Continuous Maps
163
Proofs and Comments
167
Chapter V. Topological Algebra
179
26x. Generalities on Groups
181
27x. Topological Groups
187
28x. Constructions
191
29x. Actions of Topological Groups
196
Proofs and Comments
200
Part
2.
Elements of Algebraic Topology
Chapter VI. Fundamental Group
207
30.
Homotopy
207
31.
Homotopy Properties of Path Multiplication
212
32.
Fundamental Group
215
33.
The Role of Base Point
220
Proofs and Comments
223
Chapter
VII.
Covering Spaces and Calculation of Fundamental Groups
231
34.
Covering Spaces
231
35.
Theorems on Path Lifting
235
36.
Calculation of Fundamental Groups by Using Universal
Coverings
237
Contents ix
Proofs and Comments
242
Chapter
VIII.
Fundamental Group and Maps
247
37.
Induced Homomorphisms
and Their First Applications
247
38.
Retractions and Fixed Points
253
39.
Homotopy Equivalences
256
40.
Covering Spaces via Fundamental Groups
261
41x. Classification of Covering Spaces
263
Proofs and Comments
269
Chapter IX. Cellular Techniques
279
42.
Cellular Spaces
279
43x. Topological Properties of Cellular Spaces
286
44.
Cellular Constructions
288
45.
One-Dimensional Cellular Spaces
291
46.
Fundamental Group of a Cellular Space
295
Proofs and Comments
304
Hints, Comments, Advices, Solutions, and Answers
317
Bibliography
393
Index
395 |
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| isbn | 9780821845066 |
| language | English |
| lccn | 2008009303 |
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| spelling | Elementary topology problem textbook O. Ya. Viro ... Providence, RI American Math. Soc. 2008 XX, 400 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Topologie - Manuels d'enseignement supérieur Topologie - Problèmes et exercices ram Topology Textbooks Topologie (DE-588)4060425-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Topologie (DE-588)4060425-1 s DE-604 Viro, Oleg Janovič 1948- Sonstige (DE-588)1089145128 oth Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016740663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Elementary topology problem textbook Topologie - Manuels d'enseignement supérieur Topologie - Problèmes et exercices ram Topology Textbooks Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4123623-3 |
| title | Elementary topology problem textbook |
| title_auth | Elementary topology problem textbook |
| title_exact_search | Elementary topology problem textbook |
| title_exact_search_txtP | Elementary topology problem textbook |
| title_full | Elementary topology problem textbook O. Ya. Viro ... |
| title_fullStr | Elementary topology problem textbook O. Ya. Viro ... |
| title_full_unstemmed | Elementary topology problem textbook O. Ya. Viro ... |
| title_short | Elementary topology |
| title_sort | elementary topology problem textbook |
| title_sub | problem textbook |
| topic | Topologie - Manuels d'enseignement supérieur Topologie - Problèmes et exercices ram Topology Textbooks Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topologie - Manuels d'enseignement supérieur Topologie - Problèmes et exercices Topology Textbooks Topologie Lehrbuch |
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