Topological analysis: from the basics to the triple degree for nonlinear Fredholm inclusions
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
<<De>> Gruyter
2012
|
| Schriftenreihe: | De Gruyter series in nonlinear analysis and applications
16 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | IX, 490 S. 25 cm |
| ISBN: | 9783110277227 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV040269766 | ||
| 003 | DE-604 | ||
| 005 | 20130409 | ||
| 007 | t | ||
| 008 | 120622s2012 gw |||| 00||| eng d | ||
| 015 | |a 12,N02 |2 dnb | ||
| 015 | |a 12,A24 |2 dnb | ||
| 016 | 7 | |a 1018442111 |2 DE-101 | |
| 020 | |a 9783110277227 |9 978-3-11-027722-7 | ||
| 035 | |a (OCoLC)795586436 | ||
| 035 | |a (DE-599)DNB1018442111 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-11 |a DE-19 |a DE-824 |a DE-384 |a DE-20 | ||
| 082 | 0 | |a 515.13 |2 22/ger | |
| 084 | |a SK 280 |0 (DE-625)143228: |2 rvk | ||
| 084 | |a SK 600 |0 (DE-625)143248: |2 rvk | ||
| 084 | |a SK 620 |0 (DE-625)143249: |2 rvk | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Väth, Martin |d 1967- |e Verfasser |0 (DE-588)115361499 |4 aut | |
| 245 | 1 | 0 | |a Topological analysis |b from the basics to the triple degree for nonlinear Fredholm inclusions |c Martin Väth |
| 264 | 1 | |a Berlin [u.a.] |b <<De>> Gruyter |c 2012 | |
| 300 | |a IX, 490 S. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter series in nonlinear analysis and applications |v 16 | |
| 500 | |a Literaturangaben | ||
| 650 | 0 | 7 | |a Topologische Methode |0 (DE-588)4312758-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analysis |0 (DE-588)4001865-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Analysis |0 (DE-588)4001865-9 |D s |
| 689 | 0 | 1 | |a Topologische Methode |0 (DE-588)4312758-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-11-027733-3 |
| 830 | 0 | |a De Gruyter series in nonlinear analysis and applications |v 16 |w (DE-604)BV005530011 |9 16 | |
| 856 | 4 | 2 | |m X:MVB |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=3950918&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025125373&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-025125373 | |
Datensatz im Suchindex
| _version_ | 1805146876272443392 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
PREFACE V
1 INTRODUCTION 1
1 TOPOLOGY AND MULTIVALUED M A P S
2 MULTIVALUED MAPS 9
2.1 NOTATIONS FOR MULTIVALUED MAPS AND AXIOMS 9
2.1.1 NOTATIONS 9
2.1.2 AXIOMS 11
2.2 TOPOLOGICAL NOTATIONS AND BASIC RESULTS 17
2.3 SEPARATION AXIOMS 24
2.4 UPPER SEMICONTINUOUS MULTIVALUED MAPS 43
2.5 CLOSED AND PROPER MAPS 52
2.6 COINCIDENCE POINT SETS AND CLOSED GRAPHS 55
3 METRIC SPACES 59
3.1 NOTATIONS AND BASIC RESULTS FOR METRIC SPACES 59
3.2 THREE MEASURES OF NONCOMPACTNESS 67
3.3 CONDENSING MAPS 75
3.4 CONVEXITY 84
3.5 TWO EMBEDDING THEOREMS FOR METRIC SPACES 89
3.6 SOME OLD AND NEW EXTENSION THEOREMS FOR METRIC SPACES 96
4 SPACES DEFINED BY EXTENSIONS, RETRACTIONS, OR HOMOTOPIES 105
4.1 AE AND ANE SPACES 105
4.2 ANR AND AR SPACES 107
4.3 EXTENSION OF COMPACT MAPS AND OF HOMOTOPIES 114
4.4 UV AND R$ SPACES AND HOMOTOPIC CHARACTERIZATIONS 122
5 ADVANCED TOPOLOGICAL TOOLS 129
5.1 SOME COVERING SPACE THEORY 129
HTTP://D-NB.INFO/1018442111
IMAGE 2
VIII
PREFACE
5.2 A GLIMPSE ON DIMENSION THEORY 133
5.3 VIETORIS MAPS 140
II COINCIDENCE DEGREE FOR FREDHOLM MAPS
6 SOME FUNCTIONAL ANALYSIS 147
6.1 BOUNDED LINEAR OPERATORS AND PROJECTIONS 147
6.2 LINEAR FREDHOLM OPERATORS 160
7 ORIENTATION OF FAMILIES OF LINEAR FREDHOLM OPERATORS 169
7.1 ORIENTATION OF A LINEAR FREDHOLM OPERATOR 169
7.2 ORIENTATION OF A CONTINUOUS FAMILY 178
7.3 ORIENTATION OF A FAMILY IN BANACH BUNDLES 182
8 SOME NONLINEAR ANALYSIS 197
8.1 THE POINTWISE INVERSE AND IMPLICIT FUNCTION THEOREMS 197
8.2 ORIENTED NONLINEAR FREDHOLM MAPS 203
8.3 ORIENTED FREDHOLM MAPS IN BANACH MANIFOLDS 204
8.4 A PARTIAL IMPLICIT FUNCTION THEOREM IN BANACH MANIFOLDS 214
8.5 TRANSVERSAL SUBMANIFOLDS 220
8.6 PARAMETER-DEPENDENT TRANSVERSALITY AND PARTIAL SUBMANIFOLDS . . 226
8.7 ORIENTATION ON SUBMANIFOLDS AND ON PARTIAL SUBMANIFOLDS 229
8.8 EXISTENCE OF TRANSVERSAL SUBMANIFOLDS 231
8.9 PROPERNESS OF FREDHOLM MAPS 234
9 THE BROUWER DEGREE 237
9.1 FINITE-DIMENSIONAL MANIFOLDS 237
9.2 ORIENTATION OF CONTINUOUS MAPS AND OF MANIFOLDS 248
9.3 THE C R BROUWER DEGREE 255
9.4 UNIQUENESS OF THE BROUWER DEGREE 261
9.5 EXISTENCE OF THE BROUWER DEGREE 279
9.6 SOME CLASSICAL APPLICATIONS OF THE BROUWER DEGREE 293
10 THE BENEVIERI-FURI DEGREES 309
10.1 FURTHER PROPERTIES OF THE BROUWER DEGREE 310
10.2 THE BENEVIERI-FURI C 1 DEGREE 318
IMAGE 3
PREFACE IX
10.3 THE BENEVIERI-FURI COINCIDENCE DEGREE 324
III DEGREE THEORY FOR FUNCTION TRIPLES
11 FUNCTION TRIPLES 339
11.1 FUNCTION TRIPLES AND THEIR EQUIVALENCES 341
11.2 THE SIMPLIFIER PROPERTY 355
11.3 HOMOTOPIES OF TRIPLES 361
11.4 LOCALLY NORMAL TRIPLES 365
12 THE DEGREE FOR FINITE-DIMENSIONAL FREDHOLM TRIPLES 367
12.1 THE TRIPLE VARIANT OF THE BROUWER DEGREE 367
12.2 THE TRIPLE VARIANT OF THE BENEVIERI-FURI DEGREE 380
13 THE DEGREE FOR COMPACT FREDHOLM TRIPLES 391
13.1 THE LERAY-SCHAUDER TRIPLE DEGREE 391
13.2 THE LERAY-SCHAUDER COINCIDENCE DEGREE 404
13.3 CLASSICAL APPLICATIONS OF THE LERAY-SCHAUDER DEGREE 407
14 THE DEGREE FOR NONCOMPACT FREDHOLM TRIPLES 413
14.1 THE DEGREE FOR FREDHOLM TRIPLES WITH FUNDAMENTAL SETS 414
14.2 HOMOTOPIC TESTS FOR FUNDAMENTAL SETS 429
14.3 THE DEGREE FOR FREDHOLM TRIPLES WITH CONVEX-FUNDAMENTAL SETS 437
14.4 COUNTABLY CONDENSING TRIPLES 448
14.5 CLASSICAL APPLICATIONS IN THE GENERAL FRAMEWORK 456
14.6 A SAMPLE APPLICATION FOR BOUNDARY VALUE PROBLEMS 462
BIBLIOGRAPHY 465
INDEX OF SYMBOLS - 475
INDEX 477 |
| any_adam_object | 1 |
| author | Väth, Martin 1967- |
| author_GND | (DE-588)115361499 |
| author_facet | Väth, Martin 1967- |
| author_role | aut |
| author_sort | Väth, Martin 1967- |
| author_variant | m v mv |
| building | Verbundindex |
| bvnumber | BV040269766 |
| classification_rvk | SK 280 SK 600 SK 620 |
| ctrlnum | (OCoLC)795586436 (DE-599)DNB1018442111 |
| dewey-full | 515.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.13 |
| dewey-search | 515.13 |
| dewey-sort | 3515.13 |
| 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>00000nam a2200000 cb4500</leader><controlfield tag="001">BV040269766</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130409</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">120622s2012 gw |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">12,N02</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">12,A24</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1018442111</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110277227</subfield><subfield code="9">978-3-11-027722-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)795586436</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1018442111</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="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-11</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.13</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">SK 600</subfield><subfield code="0">(DE-625)143248:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 620</subfield><subfield code="0">(DE-625)143249:</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="100" ind1="1" ind2=" "><subfield code="a">Väth, Martin</subfield><subfield code="d">1967-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)115361499</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Topological analysis</subfield><subfield code="b">from the basics to the triple degree for nonlinear Fredholm inclusions</subfield><subfield code="c">Martin Väth</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b"><<De>> Gruyter</subfield><subfield code="c">2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 490 S.</subfield><subfield code="c">25 cm</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">De Gruyter series in nonlinear analysis and applications</subfield><subfield code="v">16</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturangaben</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Topologische Methode</subfield><subfield code="0">(DE-588)4312758-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Topologische Methode</subfield><subfield code="0">(DE-588)4312758-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-11-027733-3</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">De Gruyter series in nonlinear analysis and applications</subfield><subfield code="v">16</subfield><subfield code="w">(DE-604)BV005530011</subfield><subfield code="9">16</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">X:MVB</subfield><subfield code="q">text/html</subfield><subfield code="u">http://deposit.dnb.de/cgi-bin/dokserv?id=3950918&prov=M&dok_var=1&dok_ext=htm</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB 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=025125373&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-025125373</subfield></datafield></record></collection> |
| id | DE-604.BV040269766 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-21T00:36:52Z |
| institution | BVB |
| isbn | 9783110277227 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025125373 |
| oclc_num | 795586436 |
| open_access_boolean | |
| owner | DE-11 DE-19 DE-BY-UBM DE-824 DE-384 DE-20 |
| owner_facet | DE-11 DE-19 DE-BY-UBM DE-824 DE-384 DE-20 |
| physical | IX, 490 S. 25 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | <<De>> Gruyter |
| record_format | marc |
| series | De Gruyter series in nonlinear analysis and applications |
| series2 | De Gruyter series in nonlinear analysis and applications |
| spelling | Väth, Martin 1967- Verfasser (DE-588)115361499 aut Topological analysis from the basics to the triple degree for nonlinear Fredholm inclusions Martin Väth Berlin [u.a.] <<De>> Gruyter 2012 IX, 490 S. 25 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter series in nonlinear analysis and applications 16 Literaturangaben Topologische Methode (DE-588)4312758-7 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s Topologische Methode (DE-588)4312758-7 s DE-604 Erscheint auch als Online-Ausgabe 978-3-11-027733-3 De Gruyter series in nonlinear analysis and applications 16 (DE-604)BV005530011 16 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3950918&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025125373&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Väth, Martin 1967- Topological analysis from the basics to the triple degree for nonlinear Fredholm inclusions De Gruyter series in nonlinear analysis and applications Topologische Methode (DE-588)4312758-7 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4312758-7 (DE-588)4001865-9 |
| title | Topological analysis from the basics to the triple degree for nonlinear Fredholm inclusions |
| title_auth | Topological analysis from the basics to the triple degree for nonlinear Fredholm inclusions |
| title_exact_search | Topological analysis from the basics to the triple degree for nonlinear Fredholm inclusions |
| title_full | Topological analysis from the basics to the triple degree for nonlinear Fredholm inclusions Martin Väth |
| title_fullStr | Topological analysis from the basics to the triple degree for nonlinear Fredholm inclusions Martin Väth |
| title_full_unstemmed | Topological analysis from the basics to the triple degree for nonlinear Fredholm inclusions Martin Väth |
| title_short | Topological analysis |
| title_sort | topological analysis from the basics to the triple degree for nonlinear fredholm inclusions |
| title_sub | from the basics to the triple degree for nonlinear Fredholm inclusions |
| topic | Topologische Methode (DE-588)4312758-7 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Topologische Methode Analysis |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3950918&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025125373&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005530011 |
| work_keys_str_mv | AT vathmartin topologicalanalysisfromthebasicstothetripledegreefornonlinearfredholminclusions |