Grundkurs Topologie:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Heidelberg
Spektrum Akad. Verl.
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 242 S. Ill., graph. Darst. |
| ISBN: | 9783827420404 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV035242218 | ||
| 003 | DE-604 | ||
| 005 | 20131021 | ||
| 007 | t | ||
| 008 | 090113s2009 gw ad|| |||| 00||| ger d | ||
| 015 | |a 08,N50,0928 |2 dnb | ||
| 016 | 7 | |a 991443470 |2 DE-101 | |
| 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 | |
| 028 | 5 | 2 | |a 12231416 |
| 035 | |a (OCoLC)316305302 | ||
| 035 | |a (DE-599)DNB991443470 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c XA-DE-BW | ||
| 049 | |a DE-20 |a DE-1046 |a DE-824 |a DE-92 |a DE-19 |a DE-703 |a DE-634 |a DE-91G |a DE-83 |a DE-11 |a DE-573 |a DE-29 |a DE-188 |a DE-M347 |a DE-29T |a DE-B768 |a DE-862 | ||
| 082 | 0 | |a 514 |2 22/ger | |
| 084 | |a SK 280 |0 (DE-625)143228: |2 rvk | ||
| 084 | |a 510 |2 sdnb | ||
| 084 | |a MAT 540f |2 stub | ||
| 100 | 1 | |a Laures, Gerd |e Verfasser |0 (DE-588)124580998 |4 aut | |
| 245 | 1 | 0 | |a Grundkurs Topologie |c Gerd Laures ; Markus Szymik |
| 264 | 1 | |a Heidelberg |b Spektrum Akad. Verl. |c 2009 | |
| 300 | |a X, 242 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 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 | |
| 689 | 0 | 0 | |a Topologie |0 (DE-588)4060425-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Szymik, Markus |d 1973- |e Verfasser |0 (DE-588)124918875 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017047986 | ||
Record in the Search Index
| DE-BY-FWS_katkey | 612333 |
|---|---|
| _version_ | 1824554501920522240 |
| 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- |
| author_GND | (DE-588)124580998 (DE-588)124918875 |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01747nam a2200445 c 4500</leader><controlfield tag="001">BV035242218</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20131021 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">090113s2009 gw ad|| |||| 00||| ger d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">08,N50,0928</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">991443470</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783827420404</subfield><subfield code="c">Pb. : ca. sfr 43.50 (freier Pr.), ca. EUR 27.95</subfield><subfield code="9">978-3-8274-2040-4</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9783827420404</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">12231416</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)316305302</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB991443470</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BW</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-1046</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-573</subfield><subfield code="a">DE-29</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-M347</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-B768</subfield><subfield code="a">DE-862</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514</subfield><subfield code="2">22/ger</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 280</subfield><subfield code="0">(DE-625)143228:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 540f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Laures, Gerd</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)124580998</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Grundkurs Topologie</subfield><subfield code="c">Gerd Laures ; Markus Szymik</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Heidelberg</subfield><subfield code="b">Spektrum Akad. Verl.</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 242 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topologie - Lehrbuch</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Topologie</subfield><subfield code="0">(DE-588)4060425-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Topologie</subfield><subfield code="0">(DE-588)4060425-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Szymik, Markus</subfield><subfield code="d">1973-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)124918875</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-017047986</subfield></datafield></record></collection> |
| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035242218 |
| illustrated | Illustrated |
| indexdate | 2025-02-20T06:52:47Z |
| institution | BVB |
| isbn | 9783827420404 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017047986 |
| oclc_num | 316305302 |
| open_access_boolean | |
| owner | DE-20 DE-1046 DE-824 DE-92 DE-19 DE-BY-UBM DE-703 DE-634 DE-91G DE-BY-TUM DE-83 DE-11 DE-573 DE-29 DE-188 DE-M347 DE-29T DE-B768 DE-862 DE-BY-FWS |
| owner_facet | DE-20 DE-1046 DE-824 DE-92 DE-19 DE-BY-UBM DE-703 DE-634 DE-91G DE-BY-TUM DE-83 DE-11 DE-573 DE-29 DE-188 DE-M347 DE-29T DE-B768 DE-862 DE-BY-FWS |
| 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 |