Bornological quotients:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[Bruxelles]
2005
|
| Schriftenreihe: | Mémoire de la Classe des Sciences
Collection in-4°, 3e série ; 7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 251 S. |
| ISBN: | 2803102129 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV021529303 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 060328s2005 |||| 00||| eng d | ||
| 020 | |a 2803102129 |9 2-8031-0212-9 | ||
| 035 | |a (OCoLC)67292068 | ||
| 035 | |a (DE-599)BVBBV021529303 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 | ||
| 050 | 0 | |a QA186 | |
| 100 | 1 | |a Waelbroeck, Lucien |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Bornological quotients |c Lucien Waelbroeck |
| 264 | 1 | |a [Bruxelles] |c 2005 | |
| 300 | |a 251 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mémoire de la Classe des Sciences : Collection in-4°, 3e série |v 7 | |
| 650 | 7 | |a Bornologie |2 swd | |
| 650 | 7 | |a Modulen (wiskunde) |2 gtt | |
| 650 | 7 | |a Quotient |2 swd | |
| 650 | 7 | |a Topologie |2 gtt | |
| 650 | 4 | |a Bornological spaces | |
| 650 | 4 | |a Modules (Algebra) | |
| 830 | 0 | |a Mémoire de la Classe des Sciences |v Collection in-4°, 3e série ; 7 |w (DE-604)BV021529269 |9 7 | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014745671&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014745671 | ||
Datensatz im Suchindex
| _version_ | 1804135274864705536 |
|---|---|
| adam_text | LUCIEN WAELBROECK BORNOLOGICAL QUOTIENTS WITH THE COLLABORATION OF GUY
NOEL CLASSE DES SCIENCES ACADEMIE ROYALE DE BELGIQUE CONTENTS
INTRODUCTION 7 1. THE HOLOMORPHIC FUNCTIONAL CALCULUS 7 2. THE
INTRODUCTION OF BOUNDEDNESS AND OF FORMAL QUOTIENTS 9 3. THE CONTENTS OF
THE BOOK 12 4. THE CONTRIBUTORS TO THE THEORY 14 5. .. A WORD OF
CONCLUSION 16 0 PRELIMINARIES AND NOTATIONS 17 0.1. SETS 17 0.2. SCALARS
17 0.3. ORDERED SETS 18 0.4. VECTOR SPACES 18 0.5. TOPOLOGICAL SPACES 19
0.6. TOPOLOGICAL VECTOR SPACES 20 0.7. BANACH SPACES 22 0.8. CATEGORIES
24 1 BORNOLOGICAL SPACES . 31 1.1. FUNDAMENTAL PROPERTIES OF
BORNOLOGICAL SPACES 33 1.2. EXAMPLES OF B-SPACES AND B-ALGEBRAS 53 1.3.
THE T-SEPARATED B-SPACES 64 1.4. THE STOKES THEOREM 69 1.5. THE
BUCHWALTER THEOREM 69 1.6. EXTENSION OF FUNCTORS DEFINED ON THE CATEGORY
OF BANACH SPACES 71 2 THE QUOTIENT BORNOLOGICAL SPACES 75 2.1. Q-SPACES
AND MORPHISMS 77 2.2. THE LATTICE OF Q-SUBSPACES 87 2.3. ABELIANITY AND
EXACTNESS IN Q 95 2.4. DIRECT LIMITS AND INVERSE LIMITS 102 2.5. THE
FUNCTOR (-) C 107 2.6. COMPLETION OF A QO-SPACE 107 2.7. COMMENTS 112
250 CONTENTS 3 THE TENSOR PRODUCT 115 3.1. THE Q- SPACES Q(E, F) AND Q N
(EI, ...,E N ; F) 115 3.2. THE TENSOR PRODUCT IN THE CATEGORY Q 119 3.3.
FLAT B-SPACES 129 3.4. FLATQ-SPACES 134 4 FUNCTION SPACES 137 4.1.
NORMAL SEQUENCE SPACES 138 4.2. CONTINUOUS FUNCTION SPACES 140 4.3.
MEASURABLE FUNCTION SPACES 143 4.4. NORMAL MEASURABLE FUNCTION SPACES
145 4.5. SUMMABLE AND LOCALLY SUMMABLE FUNCTION SPACES 147 4.6. THE
INTEGRAL 149 5 THE E-TENSOR PRODUCT 151 5.1. COMPACTOLOGICAL SPACES 152
5.2. GROTHENDIECK S INJECTIVE TENSOR PRODUCT 154 5.3. THE E-TENSOR
PRODUCT ON THE CATEGORY BAN 155 5.4. THE E-TENSOR PRODUCT ON THE
CATEGORIES B AND Q 159 5.5. THE E-BANACH SPACES AND THE BE-SPACES 160
5.6. EXACTNESS AND INJECTIVEBANACH SPACES 162 5.7. CONSTRUCTION OF ECO
165 5.8. THE LEFT EXACTNESS AND EXACTNESS OF EOO 168 5.9. THE FUNCTOR *
E^ * : B X Q - Q 171 5.10. COMPACT-INJECTIVEBANACH SPACES 172 5.11. G S
* ~ G EOO * IF G IS AN E-BANACH SPACE OR A BE-SPACE 173 6 NUCLEAR
B-SPACES 177 6.1. NUCLEAR MAPPINGS 178 6.2. NUCLEAR SPACES 180 6.3.
WLOKA S THEOREM 184 6.4. PERMANENCE PROPERTIES 189 6.5. THE FINE
BOUNDEDNESS 194 6.6. FUNCTION SPACES WITH VALUES IN A TENSOR PRODUCT 195
6.7. THE KOMURA-KOMURA THEOREM 204 6.8. NUCLEAR FRECHET AND NUCLEAR
SILVA SPACES 206 CONTENTS 251 7 DIFFERENTIABLE FUNCTION SPACES 211 7.1.
SPACES OF HOLDERIAN FUNCTIONS 212 7.2. SPACES OF DIFFERENTIABLE
FUNCTIONS 214 7.3. THE FUNCTOR C(/,*) 217 7.4. THE FUNCTOR C(U,-) 220
7.5. THE FUNCTORS (U, *) AND (U, *) . 221 7.6. THE FUNCTORS V(U, *)
AND V (U, *) 226 7.7. THE FUNCTORS S(&. ,-) AND S ; (R N ,-) 229 7.8.
QUOTIENTS OF NUCLEAR B-SPACES 229 BIBLIOGRAPHY 233 INDEX 241 INDEX OF
NOTATIONS 245
|
| adam_txt |
LUCIEN WAELBROECK BORNOLOGICAL QUOTIENTS WITH THE COLLABORATION OF GUY
NOEL CLASSE DES SCIENCES ACADEMIE ROYALE DE BELGIQUE CONTENTS
INTRODUCTION 7 1. THE HOLOMORPHIC FUNCTIONAL CALCULUS 7 2. THE
INTRODUCTION OF BOUNDEDNESS AND OF FORMAL QUOTIENTS 9 3. THE CONTENTS OF
THE BOOK 12 4. THE CONTRIBUTORS TO THE THEORY 14 5. . A WORD OF
CONCLUSION 16 0 PRELIMINARIES AND NOTATIONS 17 0.1. SETS 17 0.2. SCALARS
17 0.3. ORDERED SETS 18 0.4. VECTOR SPACES 18 0.5. TOPOLOGICAL SPACES 19
0.6. TOPOLOGICAL VECTOR SPACES 20 0.7. BANACH SPACES 22 0.8. CATEGORIES
24 1 BORNOLOGICAL SPACES . 31 1.1. FUNDAMENTAL PROPERTIES OF
BORNOLOGICAL SPACES 33 1.2. EXAMPLES OF B-SPACES AND B-ALGEBRAS 53 1.3.
THE T-SEPARATED B-SPACES 64 1.4. THE STOKES THEOREM 69 1.5. THE
BUCHWALTER THEOREM 69 1.6. EXTENSION OF FUNCTORS DEFINED ON THE CATEGORY
OF BANACH SPACES 71 2 THE QUOTIENT BORNOLOGICAL SPACES 75 2.1. Q-SPACES
AND MORPHISMS 77 2.2. THE LATTICE OF Q-SUBSPACES 87 2.3. ABELIANITY AND
EXACTNESS IN Q 95 2.4. DIRECT LIMITS AND INVERSE LIMITS 102 2.5. THE
FUNCTOR (-) C 107 2.6. COMPLETION OF A QO-SPACE 107 2.7. COMMENTS 112
250 CONTENTS 3 THE TENSOR PRODUCT 115 3.1. THE Q- SPACES Q(E, F) AND Q N
(EI, .,E N ; F) 115 3.2. THE TENSOR PRODUCT IN THE CATEGORY Q 119 3.3.
FLAT B-SPACES 129 3.4. FLATQ-SPACES 134 4 FUNCTION SPACES 137 4.1.
NORMAL SEQUENCE SPACES 138 4.2. CONTINUOUS FUNCTION SPACES 140 4.3.
MEASURABLE FUNCTION SPACES 143 4.4. NORMAL MEASURABLE FUNCTION SPACES
145 4.5. SUMMABLE AND LOCALLY SUMMABLE FUNCTION SPACES 147 4.6. THE
INTEGRAL 149 5 THE E-TENSOR PRODUCT 151 5.1. COMPACTOLOGICAL SPACES 152
5.2. GROTHENDIECK'S INJECTIVE TENSOR PRODUCT 154 5.3. THE E-TENSOR
PRODUCT ON THE CATEGORY BAN 155 5.4. THE E-TENSOR PRODUCT ON THE
CATEGORIES B AND Q 159 5.5. THE E-BANACH SPACES AND THE BE-SPACES 160
5.6. EXACTNESS AND INJECTIVEBANACH SPACES 162 5.7. CONSTRUCTION OF ECO
165 5.8. THE LEFT EXACTNESS AND EXACTNESS OF EOO 168 5.9. THE FUNCTOR *
E^ * : B X Q - Q 171 5.10. COMPACT-INJECTIVEBANACH SPACES 172 5.11. G S
* ~ G EOO * IF G IS AN E-BANACH SPACE OR A BE-SPACE 173 6 NUCLEAR
B-SPACES 177 6.1. NUCLEAR MAPPINGS 178 6.2. NUCLEAR SPACES 180 6.3.
WLOKA'S THEOREM 184 6.4. PERMANENCE PROPERTIES 189 6.5. THE FINE
BOUNDEDNESS 194 6.6. FUNCTION SPACES WITH VALUES IN A TENSOR PRODUCT 195
6.7. THE KOMURA-KOMURA THEOREM 204 6.8. NUCLEAR FRECHET AND NUCLEAR
SILVA SPACES 206 CONTENTS 251 7 DIFFERENTIABLE FUNCTION SPACES 211 7.1.
SPACES OF HOLDERIAN FUNCTIONS 212 7.2. SPACES OF DIFFERENTIABLE
FUNCTIONS 214 7.3. THE FUNCTOR C(/,*) 217 7.4. THE FUNCTOR C(U,-) 220
7.5. THE FUNCTORS (U, *) AND '(U, *) . 221 7.6. THE FUNCTORS V(U, *)
AND V'(U, *) 226 7.7. THE FUNCTORS S(&.",-) AND S ; (R N ,-) 229 7.8.
QUOTIENTS OF NUCLEAR B-SPACES 229 BIBLIOGRAPHY 233 INDEX 241 INDEX OF
NOTATIONS 245 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Waelbroeck, Lucien |
| author_facet | Waelbroeck, Lucien |
| author_role | aut |
| author_sort | Waelbroeck, Lucien |
| author_variant | l w lw |
| building | Verbundindex |
| bvnumber | BV021529303 |
| callnumber-first | Q - Science |
| callnumber-label | QA186 |
| callnumber-raw | QA186 |
| callnumber-search | QA186 |
| callnumber-sort | QA 3186 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)67292068 (DE-599)BVBBV021529303 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01329nam a2200373 cb4500</leader><controlfield tag="001">BV021529303</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">060328s2005 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">2803102129</subfield><subfield code="9">2-8031-0212-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)67292068</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV021529303</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</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></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA186</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Waelbroeck, Lucien</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Bornological quotients</subfield><subfield code="c">Lucien Waelbroeck</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">[Bruxelles]</subfield><subfield code="c">2005</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">251 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">Mémoire de la Classe des Sciences : Collection in-4°, 3e série</subfield><subfield code="v">7</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Bornologie</subfield><subfield code="2">swd</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Modulen (wiskunde)</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Quotient</subfield><subfield code="2">swd</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Topologie</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bornological spaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Modules (Algebra)</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mémoire de la Classe des Sciences</subfield><subfield code="v">Collection in-4°, 3e série ; 7</subfield><subfield code="w">(DE-604)BV021529269</subfield><subfield code="9">7</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV 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=014745671&sequence=000001&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:BVB01-014745671</subfield></datafield></record></collection> |
| id | DE-604.BV021529303 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:24:51Z |
| indexdate | 2024-07-09T20:37:54Z |
| institution | BVB |
| isbn | 2803102129 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014745671 |
| oclc_num | 67292068 |
| open_access_boolean | |
| owner | DE-12 |
| owner_facet | DE-12 |
| physical | 251 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| record_format | marc |
| series | Mémoire de la Classe des Sciences |
| series2 | Mémoire de la Classe des Sciences : Collection in-4°, 3e série |
| spelling | Waelbroeck, Lucien Verfasser aut Bornological quotients Lucien Waelbroeck [Bruxelles] 2005 251 S. txt rdacontent n rdamedia nc rdacarrier Mémoire de la Classe des Sciences : Collection in-4°, 3e série 7 Bornologie swd Modulen (wiskunde) gtt Quotient swd Topologie gtt Bornological spaces Modules (Algebra) Mémoire de la Classe des Sciences Collection in-4°, 3e série ; 7 (DE-604)BV021529269 7 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014745671&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Waelbroeck, Lucien Bornological quotients Mémoire de la Classe des Sciences Bornologie swd Modulen (wiskunde) gtt Quotient swd Topologie gtt Bornological spaces Modules (Algebra) |
| title | Bornological quotients |
| title_auth | Bornological quotients |
| title_exact_search | Bornological quotients |
| title_exact_search_txtP | Bornological quotients |
| title_full | Bornological quotients Lucien Waelbroeck |
| title_fullStr | Bornological quotients Lucien Waelbroeck |
| title_full_unstemmed | Bornological quotients Lucien Waelbroeck |
| title_short | Bornological quotients |
| title_sort | bornological quotients |
| topic | Bornologie swd Modulen (wiskunde) gtt Quotient swd Topologie gtt Bornological spaces Modules (Algebra) |
| topic_facet | Bornologie Modulen (wiskunde) Quotient Topologie Bornological spaces Modules (Algebra) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014745671&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021529269 |
| work_keys_str_mv | AT waelbroecklucien bornologicalquotients |