Cellular structures in topology:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Pr.
1990
|
| Edition: | 1. publ. |
| Series: | Cambridge studies in advanced mathematics
19 |
| Subjects: | |
| Online Access: | Volltext // 2015 digitalisiert von: Universitätsbibliothek der Ludwig-Maximilians-Universität München. Exemplar mit der Signatur: München, Universitätsbibliothek -- 1601/SK 300 F919 Inhaltsverzeichnis |
| Physical Description: | XI, 326 S. |
| ISBN: | 0521327849 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV004171099 | ||
| 003 | DE-604 | ||
| 005 | 20160310 | ||
| 007 | t | ||
| 008 | 901211s1990 |||| 00||| engod | ||
| 020 | |a 0521327849 |9 0-521-32784-9 | ||
| 035 | |a (OCoLC)246864772 | ||
| 035 | |a (DE-599)BVBBV004171099 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-91G |a DE-384 |a DE-739 |a DE-355 |a DE-19 |a DE-11 |a DE-M514 | ||
| 084 | |a SK 300 |0 (DE-625)143230: |2 rvk | ||
| 084 | |a MAT 546f |2 stub | ||
| 100 | 1 | |a Fritsch, Rudolf |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Cellular structures in topology |c Rudolf Fritsch ; Renzo A. Piccinini |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Pr. |c 1990 | |
| 300 | |a XI, 326 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advanced mathematics |v 19 | |
| 650 | 0 | 7 | |a CW-Komplex |0 (DE-588)4148419-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Topologie |0 (DE-588)4120861-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Simplizialer Komplex |0 (DE-588)4181492-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a CW-Komplex |0 (DE-588)4148419-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Simplizialer Komplex |0 (DE-588)4181492-7 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a CW-Komplex |0 (DE-588)4148419-8 |D s |
| 689 | 2 | 1 | |a Algebraische Topologie |0 (DE-588)4120861-4 |D s |
| 689 | 2 | |5 DE-604 | |
| 700 | 1 | |a Piccinini, Renzo A. |e Verfasser |4 aut | |
| 776 | 0 | 8 | |i Elektronische Reproduktion |d München : Universitätsbibliothek der Ludwig-Maximilians-Universität München, 2015 |o urn:nbn:de:bvb:19-epub-4493-3 |
| 830 | 0 | |a Cambridge studies in advanced mathematics |v 19 |w (DE-604)BV000003678 |9 19 | |
| 856 | 4 | 1 | |u https://nbn-resolving.org/urn:nbn:de:bvb:19-epub-4493-3 |x Resolving-System |z kostenfrei |3 Volltext // 2015 digitalisiert von: Universitätsbibliothek der Ludwig-Maximilians-Universität München. Exemplar mit der Signatur: München, Universitätsbibliothek -- 1601/SK 300 F919 |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002600508&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 912 | |a digit | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-002600508 | ||
Record in the Search Index
| _version_ | 1804118381435027456 |
|---|---|
| adam_text | Contents
Preface ix
1 The fundamental properties of CW complexes 1
1.0 Balls, spheres and projective spaces 1
1.1 Adjunction of n cells 11
1.2 CW complexes 22
1.3 Some topological properties 27
1.4 Subcomplexes 33
1.5 Finiteness and countability 40
1.6 Whitehead complexes 51
Notes 54
2 Categories of CW complexes 56
2.1 Morphisms 56
2.2 Coproducts and products 57
2.3 Some special constructions in the category CW 62
2.4 The cellular approximation theorem and some related topics 68
2.5 Whitehead s realizability theorem 76
2.6 Computation of the fundamental group 78
2.7 Increasing the connectivity of maps 83
Notes 87
3 Combinatorial complexes 89
3.1 Geometric simplices and cubes 89
3.2 Euclidean complexes 96
3.3 Simplicial complexes 109
3.4 Triangulations 128
Notes 131
4 Simplicial sets 132
4.1 The category A of finite ordinals 132
4.2 Simplicial and cosimplicial sets 139
4.3 Properties of the geometric realization functor 152
4.4 Presimplicial sets 165
4.5 Kan fibrations and Kan sets 170
4.6 Subdivision and triangulation of simplicial sets 198
Notes 220
viii Contents
5 Spaces of the type of CW complexes 223
5.1 Preliminaries 223
5.2 CW complexes and absolute neighbourhood retracts 226
5.3 n ads and function spaces 229
5.4 Spaces of the type of CW complexes and fibrations 236
Notes 239
Appendix 241
A.I Weak hausdorff /c spaces 241
A.2 Topologies determined by families of subspaces 246
A.3 Coverings 248
A.4 Cofibrations and fibrations; pushouts and pullbacks; adjunction
spaces 250
A.5 Union spaces of expanding sequences 273
A.6 Absolute neighbourhood retracts in the category of metric spaces 281
A.7 Simplicial homology 283
A.8 Homotopy groups, n connectivity, fundamental groupoid 286
A.9 Dimension and embedding 299
A. 10 The adjoint functor generating principle 303
Bibliography 306
List of symbols 313
Index 321
|
| any_adam_object | 1 |
| author | Fritsch, Rudolf Piccinini, Renzo A. |
| author_facet | Fritsch, Rudolf Piccinini, Renzo A. |
| author_role | aut aut |
| author_sort | Fritsch, Rudolf |
| author_variant | r f rf r a p ra rap |
| building | Verbundindex |
| bvnumber | BV004171099 |
| classification_rvk | SK 300 |
| classification_tum | MAT 546f |
| collection | digit |
| ctrlnum | (OCoLC)246864772 (DE-599)BVBBV004171099 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02286nam a2200493 cb4500</leader><controlfield tag="001">BV004171099</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160310 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">901211s1990 |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521327849</subfield><subfield code="9">0-521-32784-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246864772</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV004171099</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">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-M514</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 300</subfield><subfield code="0">(DE-625)143230:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 546f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Fritsch, Rudolf</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Cellular structures in topology</subfield><subfield code="c">Rudolf Fritsch ; Renzo A. Piccinini</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge u.a.</subfield><subfield code="b">Cambridge Univ. Pr.</subfield><subfield code="c">1990</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 326 S.</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="490" ind1="1" ind2=" "><subfield code="a">Cambridge studies in advanced mathematics</subfield><subfield code="v">19</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">CW-Komplex</subfield><subfield code="0">(DE-588)4148419-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Topologie</subfield><subfield code="0">(DE-588)4120861-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Simplizialer Komplex</subfield><subfield code="0">(DE-588)4181492-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">CW-Komplex</subfield><subfield code="0">(DE-588)4148419-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Simplizialer Komplex</subfield><subfield code="0">(DE-588)4181492-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">CW-Komplex</subfield><subfield code="0">(DE-588)4148419-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Algebraische Topologie</subfield><subfield code="0">(DE-588)4120861-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Piccinini, Renzo A.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Elektronische Reproduktion</subfield><subfield code="d">München : Universitätsbibliothek der Ludwig-Maximilians-Universität München, 2015</subfield><subfield code="o">urn:nbn:de:bvb:19-epub-4493-3</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Cambridge studies in advanced mathematics</subfield><subfield code="v">19</subfield><subfield code="w">(DE-604)BV000003678</subfield><subfield code="9">19</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://nbn-resolving.org/urn:nbn:de:bvb:19-epub-4493-3</subfield><subfield code="x">Resolving-System</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext // 2015 digitalisiert von: Universitätsbibliothek der Ludwig-Maximilians-Universität München. Exemplar mit der Signatur: München, Universitätsbibliothek -- 1601/SK 300 F919</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=002600508&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">digit</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-002600508</subfield></datafield></record></collection> |
| id | DE-604.BV004171099 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:09:24Z |
| institution | BVB |
| isbn | 0521327849 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002600508 |
| oclc_num | 246864772 |
| open_access_boolean | 1 |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-M514 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-M514 |
| physical | XI, 326 S. |
| psigel | digit |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Fritsch, Rudolf Verfasser aut Cellular structures in topology Rudolf Fritsch ; Renzo A. Piccinini 1. publ. Cambridge u.a. Cambridge Univ. Pr. 1990 XI, 326 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 19 CW-Komplex (DE-588)4148419-8 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Simplizialer Komplex (DE-588)4181492-7 gnd rswk-swf CW-Komplex (DE-588)4148419-8 s DE-604 Simplizialer Komplex (DE-588)4181492-7 s Algebraische Topologie (DE-588)4120861-4 s Piccinini, Renzo A. Verfasser aut Elektronische Reproduktion München : Universitätsbibliothek der Ludwig-Maximilians-Universität München, 2015 urn:nbn:de:bvb:19-epub-4493-3 Cambridge studies in advanced mathematics 19 (DE-604)BV000003678 19 https://nbn-resolving.org/urn:nbn:de:bvb:19-epub-4493-3 Resolving-System kostenfrei Volltext // 2015 digitalisiert von: Universitätsbibliothek der Ludwig-Maximilians-Universität München. Exemplar mit der Signatur: München, Universitätsbibliothek -- 1601/SK 300 F919 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002600508&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fritsch, Rudolf Piccinini, Renzo A. Cellular structures in topology Cambridge studies in advanced mathematics CW-Komplex (DE-588)4148419-8 gnd Algebraische Topologie (DE-588)4120861-4 gnd Simplizialer Komplex (DE-588)4181492-7 gnd |
| subject_GND | (DE-588)4148419-8 (DE-588)4120861-4 (DE-588)4181492-7 |
| title | Cellular structures in topology |
| title_auth | Cellular structures in topology |
| title_exact_search | Cellular structures in topology |
| title_full | Cellular structures in topology Rudolf Fritsch ; Renzo A. Piccinini |
| title_fullStr | Cellular structures in topology Rudolf Fritsch ; Renzo A. Piccinini |
| title_full_unstemmed | Cellular structures in topology Rudolf Fritsch ; Renzo A. Piccinini |
| title_short | Cellular structures in topology |
| title_sort | cellular structures in topology |
| topic | CW-Komplex (DE-588)4148419-8 gnd Algebraische Topologie (DE-588)4120861-4 gnd Simplizialer Komplex (DE-588)4181492-7 gnd |
| topic_facet | CW-Komplex Algebraische Topologie Simplizialer Komplex |
| url | https://nbn-resolving.org/urn:nbn:de:bvb:19-epub-4493-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002600508&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT fritschrudolf cellularstructuresintopology AT piccininirenzoa cellularstructuresintopology |