Grundkurs Topologie:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Heidelberg
Spektrum Akad. Verl.
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 242 S. Ill., graph. Darst. |
| ISBN: | 9783827420404 |
Internformat
MARC
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| 020 | |a 9783827420404 |c Pb. : ca. sfr 43.50 (freier Pr.), ca. EUR 27.95 |9 978-3-8274-2040-4 | ||
| 024 | 3 | |a 9783827420404 | |
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| 264 | 1 | |a Heidelberg |b Spektrum Akad. Verl. |c 2009 | |
| 300 | |a X, 242 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Topologie - Lehrbuch | |
| 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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Datensatz im Suchindex
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|---|---|
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| adam_text | Inhaltsverzeichnis
Vorwort................................................................
VI
1 Grundbegriffe der
Topologie
....................................... 1
1.1 Metrische Räume..................................................... 1
1.2
Topologische
Räume.................................................. 7
1.3 Abgeschlossene Teilmengen............................................ 11
1.4 Die Kategoriensprache................................................ 14
2 Universelle Konstruktionen........................................ 19
2.1 Teilräume........................................................... 19
2.2 Produkte............................................................ 24
2.3 Summen............................................................ 28
2.4 Identifizierungen und Quotienten....................................... 30
3 Zusammenhang und Trennung..................................... 41
3.1 Zusammenhang...................................................... 41
3.2 Trennung und stetige Fortsetzbarkeit................................... 47
4 Kompaktheit und Abbildungsräume ............................... 55
4.1 Kompaktheit........................................................ 55
4.2 Eigentliche Abbildungen.............................................. 64
4.3 Der Satz von Tychonoff............................................... 68
4.4 Abbildungsräume.................................................... 71
4.5 Lokal kompakt erzeugte Räume........................................ 77
5 Transformationsgruppen........................................... 83
5.1 Grundbegriffe der äquivarianten
Topologie
............................... 83
5.2 Homogene Räume.................................................... 88
5.3 Eigentliche Operationen................................................ 93
6 Wege und Schleifen................................................ 99
6.1 Wegeräume und Schleifenräume........................................ 99
6.2 Der Wegekomponentenfunktor......................................... 103
6.3 Der
Homotopiebegriff
................................................. 108
6.4 Selbstabbildungen des Kreises.......................................... 114
7 Die Fundamentalgruppe ........................................... 123
7.1 Das Pundamentalgruppoid............................................. 123
7.2 Der Satz von Seifert und van Kampen.................................. 133
7.3 Flächen............................................................. 144
8 Überlagerungen.................................................... 153
8.1 Die Kategorie der Überlagerungen...................................... 153
8.2 Der Hochhebungssatz................................................. 161
Inhaltsverzeichnis
8.3 Fasertransport....................................................... 164
8.4 Der Klassifikationssatz................................................ 169
8.5
Topologische
Galois-Theorie........................................... 172
9 Bündel und Faserungen............................................ 183
9.1 Faserbündel......................................................... 183
9.2 Prinzipalbündel...................................................... 189
9.3 Prinzipalbündel mit diskreter Strukturgruppe............................ 193
9.4 Vektorraumbündel.................................................... 196
9.5 Faserungen.......................................................... 199
10 Garben............................................................207
10.1 Prägarben und Garben ...............................................207
10.2 Halme und Etalräume................................................210
10.3 Garbifizierung und Pullbacks..........................................214
11 Simpliziale Mengen................................................217
11.1 Simpliziale Objekte und Morphismen...................................217
11.2
Singulare Simplizes
und Realisierungen .................................222
11.3 Ausblicke ...........................................................230
Literaturverzeichnis ....................................................237
Index...................................................................239
|
| any_adam_object | 1 |
| author | Laures, Gerd Szymik, Markus 1973- |
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| author_facet | Laures, Gerd Szymik, Markus 1973- |
| author_role | aut aut |
| author_sort | Laures, Gerd |
| author_variant | g l gl m s ms |
| building | Verbundindex |
| bvnumber | BV035242218 |
| classification_rvk | SK 280 |
| classification_tum | MAT 540f |
| ctrlnum | (OCoLC)316305302 (DE-599)DNB991443470 |
| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035242218 |
| illustrated | Illustrated |
| indexdate | 2024-08-01T12:12:42Z |
| institution | BVB |
| isbn | 9783827420404 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017047986 |
| oclc_num | 316305302 |
| open_access_boolean | |
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| physical | X, 242 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Spektrum Akad. Verl. |
| record_format | marc |
| spellingShingle | Laures, Gerd Szymik, Markus 1973- Grundkurs Topologie Topologie - Lehrbuch Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4123623-3 |
| title | Grundkurs Topologie |
| title_auth | Grundkurs Topologie |
| title_exact_search | Grundkurs Topologie |
| title_full | Grundkurs Topologie Gerd Laures ; Markus Szymik |
| title_fullStr | Grundkurs Topologie Gerd Laures ; Markus Szymik |
| title_full_unstemmed | Grundkurs Topologie Gerd Laures ; Markus Szymik |
| title_short | Grundkurs Topologie |
| title_sort | grundkurs topologie |
| topic | Topologie - Lehrbuch Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topologie - Lehrbuch Topologie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017047986&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lauresgerd grundkurstopologie AT szymikmarkus grundkurstopologie |