Topological groups and the Pontryagin-van Kampen duality: an introduction
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
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Berlin/Boston
De Gruyter
[2022]
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| Series: | De Gruyter studies in mathematics
Volume 83 |
| Subjects: | |
| Online Access: | https://www.degruyter.com/isbn/9783110653496 Inhaltsverzeichnis |
| Physical Description: | XIV, 376 Seiten 24 cm x 17 cm, 789 g |
| ISBN: | 9783110653496 3110653494 |
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| 245 | 1 | 0 | |a Topological groups and the Pontryagin-van Kampen duality |b an introduction |c Lydia Außenhofer, Dikran Dikranjan, and Anna Giordano Bruno |
| 264 | 1 | |a Berlin/Boston |b De Gruyter |c [2022] | |
| 264 | 4 | |c © 2022 | |
| 300 | |a XIV, 376 Seiten |c 24 cm x 17 cm, 789 g | ||
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| 653 | |a Lokal kompakte Abelsche Gruppe | ||
| 653 | |a Pontrjagin-Dualität | ||
| 653 | |a Topologische Gruppe | ||
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Record in the Search Index
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| adam_text | Contents Preface—V 1 Introduction — 1 շ 2.1 2.1.1 2.1.2 2.1.3 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.3 2.4 2.5 Definition and examples — 7 Basic definitions and properties — 7 Definition---- 7 The neighborhood filter of the neutral element---- 8 Comparing group topologies-----12 Examples of group topologies------ 13 Linear topologies and functorial topologies---- 13 Topologies generated by characters---- 14 Interrelations among functorial topologies---- 16 The pointwise convergence topology---- 19 Semitopological, paratopological, and quasitopological groups-----20 Exercises---- 21 Further readings, notes, and comments---- 24 3 3.1 3.1.1 3.1.2 3.1.3 3.2 3.3 3.4 3.5 General properties of topological groups — 27 Subgroups and separation---- 27 Closed and dense subgroups----- 28 Separation axioms---- 31 Extension of identities in Hausdorff groups---- 33 Quotients of topological groups---- 34 Initial and final topologies: products of topological groups---- 40 The Hausdorff reflectionof a topological group----- 43 Exercises---- 46 4 4.1 4.2 4.3 4.4 4.5 4.6 Markov’s problems---- 51 The Zariski and Markov topologies---- 51 The Markov topology of the symmetric group---- 52 Existence of Hausdorff group topologies---- 56 Extension of group topologies---- 59 Exercises---- 62 Further readings, notes, and comments----- 65 5 5.1 5.2 5.2.1 Cardinal invariants and metrizability — 67 Cardinal invariants of topological groups---- 67 Metrizability of topological groups---- 72 Pseudonorms and invariant pseudometrics in a group---- 72
x 5.2.2 5.2.3 5.2.4 5.3 5.3.1 5.3.2 5.3.3 5.4 Contents Continuous pseudonorms and pseudometrics — 75 The Birkhoff-Kakutani theorem------78 Function spaces as topological groups-----79 Topologies and subgroups determined by sequences-----81 7-sequences-----81 Topologically torsion elements and subgroups-----82 Characterization of 7-sequences------83 Exercises---- 86 6 6.1 6.2 6.3 Connectedness in topological groups — 91 Connected and hereditarily disconnected groups-----91 The four components-----93 Exercises----- 95 7 7.1 7.1.1 7.1.2 7.1.3 7.2 7.2.1 7.2.2 7.2.3 7.3 Completeness and completion — 97 Completeness and completion via Cauchy nets — 97 Cauchy nets and completeness----- 97 Completion via Cauchy nets------99 Weil completion-----105 Completeness via filters----- 107 Cauchy filters-----107 Minimal Cauchy filters--- 108 Completeness of the linearly topologized groups-----111 Exercises----- 112 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 Compactness and local compactness - a first encounter —115 Examples-----115 Specific properties of compactness and local compactness —117 Compactly generated locally compact groups —119 The open mapping theorem------121 Compactness vs connectedness------122 The Bohr compactification---124 Exercises----- 126 Further readings, notes, and comments-----128 9 9.1 9.2 9.3 9.4 9.4.1 Properties of Жп and its subgroups-----131 Lifting homomorphisms with domain Ж -----131 The closed subgroups of R°-----133 The second proof of Theorem 9.2.2-----135 Elementary LCA groups and the Kronecker theorem —138 Quotients of R and closed subgroups of Tk----- 138 9.4.2
Closure in R -----139
Contents 95 Exercises----- 141 10 Subgroups of compact groups —143 10.1 Big subsets of groups-----143 10.2 Precompact groups-----145 10.2.1 Totally bounded and precompact groups-----145 10.2.2 A second (internal) approach to the Bohr compactification —149 10.2.3 Precompactness of the topologies induced by characters-----150 10.3 Unitary representations of locally compact groups-----151 10.4 10.5 11 11.1 11.2 11.3 11.3.1 11.3.2 11.4 11.5 11.6 11.7 11.8 Exercises-----154 Further readings, notes, and comments------156 The Følner theorem-----159 Fourier theory for finite abelian groups-----159 The Bogoliouboff and Følner lemmas-----161 The Prodanov lemma and independence of characters---- 168 The Prodanov lemma and the Følner theorem-----169 Independence of characters —174 Precompact group topologies on abelian groups-----175 The Peter-Weyl theorem for compact abelian groups-----177 On the structure of compactly generated LCAgroups----- 179 Exercises-----184 Further readings, notes, and comments------185 12 Almost periodic functions and Haar integrals —187 12.1 Almost periodic functions-----187 12.1.1 The algebra of almost periodic functions-----187 12.1.2 Almost periodic functions and the Bohr compactification of abelian groups-----189 12.2 The Haar integral —193 12.2.1 The Haar integral for almost periodic functions on topological abelian groups-----193 12.2.2 The Haar integral on LCAgroups-----194 12.2.3 The Haar integral of locally compact groups-----197 12.3 Exercises-----198 12.4 Further readings, notes, and comments-----199 13 The Pontryagin-van Kampen duality-----201
13.1 The dual group-----201 13.2 Computation of some dual groups-----204 13.3 Some general properties of the dual group-----207 13.3.1 The dual of direct products and direct sums------207 XI
XII — Contents 13.3.2 Extending the duality functor to homomorphisms — 209 13.4 The natural transformation ω-----212 13.4.1 The compact or discrete case---- 214 13.4.2 Exactness of the duality functor----- 216 13.4.3 Proof of the Pontryagin-van Kampen duality theorem----- 219 13.5 Further properties of the annihilators----- 220 13.6 Duality for precompact abelian groups — 222 13.7 Exercises----- 223 13.8 Further readings, notes, and comments----- 225 14 Applications of the duality theorem — 229 14.1 The structure of compact abelian groups----- 229 14.2 The structure of LCA groups----- 232 14.2.1 The subgroup of compact elements of an LCA group----- 232 14.2.2 The structure theory of LCA groups------ 234 14.3 Topological features of LCA groups------ 238 14.3.1 Dimension of locally compact groups------ 238 14.3.2 The Halmos problem: the algebraic structure of compact abelian 14.3.3 The Bohr topology of abelian groups — 248 groups----- 245 14.4 Precompact group topologies determined by sequences----- 252 14.4.1 Characterized subgroups of T----- 252 14.4.2 Characterized subgroups of topological abelian groups----- 254 14.4.3 TB-sequences----- 256 14.5 Exercises----- 258 14.6 Further readings, notes, and comments-----261 15 Pseudocompact groups----- 263 15.1 General properties of countably compact and pseudocompact 15.2 spaces — 263 The Comfort-Ross criterion for pseudocompact groups----- 265 15.2.1 The Comfort-Ross criterion and first applications----- 265 15.2.2 The G0-refinement andits relation to pseudocompact groups------ 266 15.3 C-embedded subsets and Moscow spaces------
268 15.3.1 C- and C*-embedded subgroups and subspaces----- 268 15.3.2 R-factorizable groups and Moscow spaces----- 271 15.3.3 Submetrizable pseudocompact groups are compact — 271 15.4 Exercises----- 272 15.5 Further readings, notes, and comments------273 16 16.1 Topological rings, fields, and modules — 275 Topological rings and fields------ 275
Contents 16.1.1 16.1.2 16.2 16.2.1 16.2.2 16.2.3 16.3 16.4 A Examples and general properties of topological rings-----276 Topological fields-----277 Topological modules-----278 Uniqueness of the Pontryagin-van Kampen duality-----279 Locally linearly compact modules-----283 The Lefschetz-Kaplansky-MacDonald duality — 285 Exercises-----287 Further readings, notes, and comments-----289 A.4.1 A.4.2 A.4.3 A.5 A. 6 A .7 Background on groups — 291 Torsion abelian groups and torsion-free abelian groups-----292 Divisible abelian groups------ 294 Free abelian groups----- 298 Reduced abelian groups------ 300 Residually finite groups----- 302 The p-adic integers--------- 305 Indecomposable abelian groups------307 Extensions of abelian groups------307 Nonabelian groups---------311 Exercises------312 В Background on topological spaces — 315 A.l A.2 A.3 A.4 B. l B.1.1 B.l.2 B.1.3 B.2 B.2.1 B.2.2 B.2.3 B.3 B.3.1 B.3.2 B.3.3 B.3.4 B.4 B.5 B.5.1 B.5.2 B.5.3 B.5.4 B.6 XIII Basic definitions---------315 Filters------315 Topologies, bases, prebases, and neighborhoods — 316 Ordering topologies, closure, and interior-----317 Convergent nets and filters------319 Convergent sequences------319 Convergent nets---------319 Convergent filters------321 Continuous maps and cardinal invariants of topological spaces — 322 Continuous maps and their properties-----322 Metric spaces and the open ball topology----- 323 Cardinal invariants---------325 Borei sets, zero-sets, and Baire sets------326 Subspace, quotient, product, and coproduct topologies-----327 Separation axioms and compactness-like properties —
329 Separation axioms---------329 Compactness-like properties----- 330 Relations among compactness-like properties----- 333 The Stone-Weierstraß theorem----- 334 Connected and hereditarily disconnected spaces-----335
XIV — Contents B. 7 С C. 1 C.2 C.2.1 C.2.2 C.2.3 C.3 Exercises------337 Background on categories and functors — 341 Categori es------341 Functors------344 Reflectors and coreflectors-------346 Reflectors and coreflectors vs (pre)radicals in AbGrp — 348 Contravariant Hom-functors — 350 Exercises------352 Bibliography — 357 Index of symbols----- 369 Index----- 371
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| adam_txt |
Contents Preface—V 1 Introduction — 1 շ 2.1 2.1.1 2.1.2 2.1.3 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.3 2.4 2.5 Definition and examples — 7 Basic definitions and properties — 7 Definition---- 7 The neighborhood filter of the neutral element---- 8 Comparing group topologies-----12 Examples of group topologies------ 13 Linear topologies and functorial topologies---- 13 Topologies generated by characters---- 14 Interrelations among functorial topologies---- 16 The pointwise convergence topology---- 19 Semitopological, paratopological, and quasitopological groups-----20 Exercises---- 21 Further readings, notes, and comments---- 24 3 3.1 3.1.1 3.1.2 3.1.3 3.2 3.3 3.4 3.5 General properties of topological groups — 27 Subgroups and separation---- 27 Closed and dense subgroups----- 28 Separation axioms---- 31 Extension of identities in Hausdorff groups---- 33 Quotients of topological groups---- 34 Initial and final topologies: products of topological groups---- 40 The Hausdorff reflectionof a topological group----- 43 Exercises---- 46 4 4.1 4.2 4.3 4.4 4.5 4.6 Markov’s problems---- 51 The Zariski and Markov topologies---- 51 The Markov topology of the symmetric group---- 52 Existence of Hausdorff group topologies---- 56 Extension of group topologies---- 59 Exercises---- 62 Further readings, notes, and comments----- 65 5 5.1 5.2 5.2.1 Cardinal invariants and metrizability — 67 Cardinal invariants of topological groups---- 67 Metrizability of topological groups---- 72 Pseudonorms and invariant pseudometrics in a group---- 72
x 5.2.2 5.2.3 5.2.4 5.3 5.3.1 5.3.2 5.3.3 5.4 Contents Continuous pseudonorms and pseudometrics — 75 The Birkhoff-Kakutani theorem------78 Function spaces as topological groups-----79 Topologies and subgroups determined by sequences-----81 7-sequences-----81 Topologically torsion elements and subgroups-----82 Characterization of 7-sequences------83 Exercises---- 86 6 6.1 6.2 6.3 Connectedness in topological groups — 91 Connected and hereditarily disconnected groups-----91 The four components-----93 Exercises----- 95 7 7.1 7.1.1 7.1.2 7.1.3 7.2 7.2.1 7.2.2 7.2.3 7.3 Completeness and completion — 97 Completeness and completion via Cauchy nets — 97 Cauchy nets and completeness----- 97 Completion via Cauchy nets------99 Weil completion-----105 Completeness via filters----- 107 Cauchy filters-----107 Minimal Cauchy filters--- 108 Completeness of the linearly topologized groups-----111 Exercises----- 112 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 Compactness and local compactness - a first encounter —115 Examples-----115 Specific properties of compactness and local compactness —117 Compactly generated locally compact groups —119 The open mapping theorem------121 Compactness vs connectedness------122 The Bohr compactification---124 Exercises----- 126 Further readings, notes, and comments-----128 9 9.1 9.2 9.3 9.4 9.4.1 Properties of Жп and its subgroups-----131 Lifting homomorphisms with domain Ж"-----131 The closed subgroups of R°-----133 The second proof of Theorem 9.2.2-----135 Elementary LCA groups and the Kronecker theorem —138 Quotients of R" and closed subgroups of Tk----- 138 9.4.2
Closure in R"-----139
Contents 95 Exercises----- 141 10 Subgroups of compact groups —143 10.1 Big subsets of groups-----143 10.2 Precompact groups-----145 10.2.1 Totally bounded and precompact groups-----145 10.2.2 A second (internal) approach to the Bohr compactification —149 10.2.3 Precompactness of the topologies induced by characters-----150 10.3 Unitary representations of locally compact groups-----151 10.4 10.5 11 11.1 11.2 11.3 11.3.1 11.3.2 11.4 11.5 11.6 11.7 11.8 Exercises-----154 Further readings, notes, and comments------156 The Følner theorem-----159 Fourier theory for finite abelian groups-----159 The Bogoliouboff and Følner lemmas-----161 The Prodanov lemma and independence of characters---- 168 The Prodanov lemma and the Følner theorem-----169 Independence of characters —174 Precompact group topologies on abelian groups-----175 The Peter-Weyl theorem for compact abelian groups-----177 On the structure of compactly generated LCAgroups----- 179 Exercises-----184 Further readings, notes, and comments------185 12 Almost periodic functions and Haar integrals —187 12.1 Almost periodic functions-----187 12.1.1 The algebra of almost periodic functions-----187 12.1.2 Almost periodic functions and the Bohr compactification of abelian groups-----189 12.2 The Haar integral —193 12.2.1 The Haar integral for almost periodic functions on topological abelian groups-----193 12.2.2 The Haar integral on LCAgroups-----194 12.2.3 The Haar integral of locally compact groups-----197 12.3 Exercises-----198 12.4 Further readings, notes, and comments-----199 13 The Pontryagin-van Kampen duality-----201
13.1 The dual group-----201 13.2 Computation of some dual groups-----204 13.3 Some general properties of the dual group-----207 13.3.1 The dual of direct products and direct sums------207 XI
XII — Contents 13.3.2 Extending the duality functor to homomorphisms — 209 13.4 The natural transformation ω-----212 13.4.1 The compact or discrete case---- 214 13.4.2 Exactness of the duality functor----- 216 13.4.3 Proof of the Pontryagin-van Kampen duality theorem----- 219 13.5 Further properties of the annihilators----- 220 13.6 Duality for precompact abelian groups — 222 13.7 Exercises----- 223 13.8 Further readings, notes, and comments----- 225 14 Applications of the duality theorem — 229 14.1 The structure of compact abelian groups----- 229 14.2 The structure of LCA groups----- 232 14.2.1 The subgroup of compact elements of an LCA group----- 232 14.2.2 The structure theory of LCA groups------ 234 14.3 Topological features of LCA groups------ 238 14.3.1 Dimension of locally compact groups------ 238 14.3.2 The Halmos problem: the algebraic structure of compact abelian 14.3.3 The Bohr topology of abelian groups — 248 groups----- 245 14.4 Precompact group topologies determined by sequences----- 252 14.4.1 Characterized subgroups of T----- 252 14.4.2 Characterized subgroups of topological abelian groups----- 254 14.4.3 TB-sequences----- 256 14.5 Exercises----- 258 14.6 Further readings, notes, and comments-----261 15 Pseudocompact groups----- 263 15.1 General properties of countably compact and pseudocompact 15.2 spaces — 263 The Comfort-Ross criterion for pseudocompact groups----- 265 15.2.1 The Comfort-Ross criterion and first applications----- 265 15.2.2 The G0-refinement andits relation to pseudocompact groups------ 266 15.3 C-embedded subsets and Moscow spaces------
268 15.3.1 C- and C*-embedded subgroups and subspaces----- 268 15.3.2 R-factorizable groups and Moscow spaces----- 271 15.3.3 Submetrizable pseudocompact groups are compact — 271 15.4 Exercises----- 272 15.5 Further readings, notes, and comments------273 16 16.1 Topological rings, fields, and modules — 275 Topological rings and fields------ 275
Contents 16.1.1 16.1.2 16.2 16.2.1 16.2.2 16.2.3 16.3 16.4 A Examples and general properties of topological rings-----276 Topological fields-----277 Topological modules-----278 Uniqueness of the Pontryagin-van Kampen duality-----279 Locally linearly compact modules-----283 The Lefschetz-Kaplansky-MacDonald duality — 285 Exercises-----287 Further readings, notes, and comments-----289 A.4.1 A.4.2 A.4.3 A.5 A. 6 A .7 Background on groups — 291 Torsion abelian groups and torsion-free abelian groups-----292 Divisible abelian groups------ 294 Free abelian groups----- 298 Reduced abelian groups------ 300 Residually finite groups----- 302 The p-adic integers--------- 305 Indecomposable abelian groups------307 Extensions of abelian groups------307 Nonabelian groups---------311 Exercises------312 В Background on topological spaces — 315 A.l A.2 A.3 A.4 B. l B.1.1 B.l.2 B.1.3 B.2 B.2.1 B.2.2 B.2.3 B.3 B.3.1 B.3.2 B.3.3 B.3.4 B.4 B.5 B.5.1 B.5.2 B.5.3 B.5.4 B.6 XIII Basic definitions---------315 Filters------315 Topologies, bases, prebases, and neighborhoods — 316 Ordering topologies, closure, and interior-----317 Convergent nets and filters------319 Convergent sequences------319 Convergent nets---------319 Convergent filters------321 Continuous maps and cardinal invariants of topological spaces — 322 Continuous maps and their properties-----322 Metric spaces and the open ball topology----- 323 Cardinal invariants---------325 Borei sets, zero-sets, and Baire sets------326 Subspace, quotient, product, and coproduct topologies-----327 Separation axioms and compactness-like properties —
329 Separation axioms---------329 Compactness-like properties----- 330 Relations among compactness-like properties----- 333 The Stone-Weierstraß theorem----- 334 Connected and hereditarily disconnected spaces-----335
XIV — Contents B. 7 С C. 1 C.2 C.2.1 C.2.2 C.2.3 C.3 Exercises------337 Background on categories and functors — 341 Categori es------341 Functors------344 Reflectors and coreflectors-------346 Reflectors and coreflectors vs (pre)radicals in AbGrp — 348 Contravariant Hom-functors — 350 Exercises------352 Bibliography — 357 Index of symbols----- 369 Index----- 371 |
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| any_adam_object_boolean | 1 |
| author | Außenhofer, Lydia ca. 20./21. Jh Dikranjan, Dikran N. 1950- Giordano Bruno, Anna |
| author_GND | (DE-588)1246142465 (DE-588)172044308 (DE-588)1218558172 |
| author_facet | Außenhofer, Lydia ca. 20./21. Jh Dikranjan, Dikran N. 1950- Giordano Bruno, Anna |
| author_role | aut aut aut |
| author_sort | Außenhofer, Lydia ca. 20./21. Jh |
| author_variant | l a la d n d dn dnd b a g ba bag |
| building | Verbundindex |
| bvnumber | BV047603797 |
| classification_rvk | SK 340 |
| ctrlnum | (OCoLC)1286872792 (DE-599)DNB123681505X |
| discipline | Mathematik |
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| id | DE-604.BV047603797 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:37:33Z |
| indexdate | 2024-07-10T09:15:56Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110653496 3110653494 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032988842 |
| oclc_num | 1286872792 |
| open_access_boolean | |
| owner | DE-739 DE-11 DE-29T DE-188 |
| owner_facet | DE-739 DE-11 DE-29T DE-188 |
| physical | XIV, 376 Seiten 24 cm x 17 cm, 789 g |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Außenhofer, Lydia ca. 20./21. Jh. Verfasser (DE-588)1246142465 aut Topological groups and the Pontryagin-van Kampen duality an introduction Lydia Außenhofer, Dikran Dikranjan, and Anna Giordano Bruno Berlin/Boston De Gruyter [2022] © 2022 XIV, 376 Seiten 24 cm x 17 cm, 789 g txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics Volume 83 Topologische Gruppe (DE-588)4135793-0 gnd rswk-swf Dualität (DE-588)4013161-0 gnd rswk-swf Lokal kompakte Abelsche Gruppe Pontrjagin-Dualität Topologische Gruppe Topologische Gruppe (DE-588)4135793-0 s Dualität (DE-588)4013161-0 s DE-604 Dikranjan, Dikran N. 1950- Verfasser (DE-588)172044308 aut Giordano Bruno, Anna Verfasser (DE-588)1218558172 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-065493-6 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-065355-7 De Gruyter studies in mathematics Volume 83 (DE-604)BV000005407 83 X:MVB https://www.degruyter.com/isbn/9783110653496 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032988842&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Außenhofer, Lydia ca. 20./21. Jh Dikranjan, Dikran N. 1950- Giordano Bruno, Anna Topological groups and the Pontryagin-van Kampen duality an introduction De Gruyter studies in mathematics Topologische Gruppe (DE-588)4135793-0 gnd Dualität (DE-588)4013161-0 gnd |
| subject_GND | (DE-588)4135793-0 (DE-588)4013161-0 |
| title | Topological groups and the Pontryagin-van Kampen duality an introduction |
| title_auth | Topological groups and the Pontryagin-van Kampen duality an introduction |
| title_exact_search | Topological groups and the Pontryagin-van Kampen duality an introduction |
| title_exact_search_txtP | Topological groups and the Pontryagin-van Kampen duality an introduction |
| title_full | Topological groups and the Pontryagin-van Kampen duality an introduction Lydia Außenhofer, Dikran Dikranjan, and Anna Giordano Bruno |
| title_fullStr | Topological groups and the Pontryagin-van Kampen duality an introduction Lydia Außenhofer, Dikran Dikranjan, and Anna Giordano Bruno |
| title_full_unstemmed | Topological groups and the Pontryagin-van Kampen duality an introduction Lydia Außenhofer, Dikran Dikranjan, and Anna Giordano Bruno |
| title_short | Topological groups and the Pontryagin-van Kampen duality |
| title_sort | topological groups and the pontryagin van kampen duality an introduction |
| title_sub | an introduction |
| topic | Topologische Gruppe (DE-588)4135793-0 gnd Dualität (DE-588)4013161-0 gnd |
| topic_facet | Topologische Gruppe Dualität |
| url | https://www.degruyter.com/isbn/9783110653496 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032988842&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
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