Holdings: Bornological quotients

Bornological quotients:

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Bibliographic Details
Main Author:	Waelbroeck, Lucien (Author)
Format:	Book
Language:	English
Published:	[Bruxelles] 2005
Series:	Mémoire de la Classe des Sciences Collection in-4°, 3e série ; 7
Subjects:	Bornologie Modulen (wiskunde) Quotient Topologie Bornological spaces Modules (Algebra)
Online Access:	Inhaltsverzeichnis
Physical Description:	251 S.
ISBN:	2803102129

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MARC


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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
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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)
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