Pontryagin duality and the structure of locally compact abelian groups /:
These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amo...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1977.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
29. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses. |
| Beschreibung: | 1 online resource (viii, 128 pages) |
| Bibliographie: | Includes bibliographical references (pages 119-120) and index. |
| ISBN: | 9781107360877 1107360870 9780511600722 0511600720 |
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| 245 | 1 | 0 | |a Pontryagin duality and the structure of locally compact abelian groups / |c Sidney A. Morris. |
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 29 | |
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| 505 | 8 | |a 7. Consequences of the duality theoremExercise Set Fourteen; Exercise Set Fifteen; 8. Locally Euclidean and NSS-groups; Exercise Set Sixteen; 9. Non-abelian groups; References; Index of terms; Index of Exercises, propositions and theorems | |
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| contents | Cover; Title; Copyright; Contents; Preface; 1. Introduction to topological groups; Exercise set one; Exercise Set Two; Exercise Set Three; Exercise Set Four; 2. Subgroups and quotient groups of Rn; Exercise Set Five; 3. Uniform spaces and dual groups; Exercise Set Six; Exercise Set Seven; 4. Introduction to the Pontryagin-van Kampen duality theorem; Exercise Set Eight; Exercise Set Nine; 5. Duality for compact and discrete groups; Exercise Set Ten; Exercise Set Eleven; 6. The duality theorem and the principal structure theorem; Exercise Set Twelve; Exercise Set Thirteen 7. Consequences of the duality theoremExercise Set Fourteen; Exercise Set Fifteen; 8. Locally Euclidean and NSS-groups; Exercise Set Sixteen; 9. Non-abelian groups; References; Index of terms; Index of Exercises, propositions and theorems |
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| id | ZDB-4-EBA-ocn836870848 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
| institution | BVB |
| isbn | 9781107360877 1107360870 9780511600722 0511600720 |
| language | English |
| oclc_num | 836870848 |
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| spelling | Morris, Sidney A., 1947- https://id.oclc.org/worldcat/entity/E39PCjrHHXg8Wy3j3Kw8vY7Dtq http://id.loc.gov/authorities/names/n98061088 Pontryagin duality and the structure of locally compact abelian groups / Sidney A. Morris. Cambridge ; New York : Cambridge University Press, 1977. 1 online resource (viii, 128 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 29 Includes bibliographical references (pages 119-120) and index. Print version record. These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses. Cover; Title; Copyright; Contents; Preface; 1. Introduction to topological groups; Exercise set one; Exercise Set Two; Exercise Set Three; Exercise Set Four; 2. Subgroups and quotient groups of Rn; Exercise Set Five; 3. Uniform spaces and dual groups; Exercise Set Six; Exercise Set Seven; 4. Introduction to the Pontryagin-van Kampen duality theorem; Exercise Set Eight; Exercise Set Nine; 5. Duality for compact and discrete groups; Exercise Set Ten; Exercise Set Eleven; 6. The duality theorem and the principal structure theorem; Exercise Set Twelve; Exercise Set Thirteen 7. Consequences of the duality theoremExercise Set Fourteen; Exercise Set Fifteen; 8. Locally Euclidean and NSS-groups; Exercise Set Sixteen; 9. Non-abelian groups; References; Index of terms; Index of Exercises, propositions and theorems Locally compact Abelian groups. http://id.loc.gov/authorities/subjects/sh85077961 Duality theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85039851 Pontrjagin duality. http://id.loc.gov/authorities/subjects/sh2010014118 Abel, Groupes localement compacts d' Dualité, Théorie de la (Mathématiques) Groupes abéliens localement compacts. Principe de dualité (Mathématiques) Dualité de Pontrjagin. MATHEMATICS Algebra Linear. bisacsh Duality theory (Mathematics) fast Locally compact Abelian groups fast Pontrjagin duality fast Lokal kompakte Abelsche Gruppe gnd http://d-nb.info/gnd/4168093-5 Pontrjagin-Dualität gnd http://d-nb.info/gnd/4365532-4 has work: Pontryagin duality and the structure of locally compact abelian groups (Text) https://id.oclc.org/worldcat/entity/E39PCFCbMvbYqm3JWRhgHrF8Q3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Morris, Sidney A., 1947- Pontryagin duality and the structure of locally compact abelian groups. Cambridge ; New York : Cambridge University Press, 1977 0521215439 (DLC) 76053519 (OCoLC)2695002 London Mathematical Society lecture note series ; 29. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552425 Volltext |
| spellingShingle | Morris, Sidney A., 1947- Pontryagin duality and the structure of locally compact abelian groups / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; Preface; 1. Introduction to topological groups; Exercise set one; Exercise Set Two; Exercise Set Three; Exercise Set Four; 2. Subgroups and quotient groups of Rn; Exercise Set Five; 3. Uniform spaces and dual groups; Exercise Set Six; Exercise Set Seven; 4. Introduction to the Pontryagin-van Kampen duality theorem; Exercise Set Eight; Exercise Set Nine; 5. Duality for compact and discrete groups; Exercise Set Ten; Exercise Set Eleven; 6. The duality theorem and the principal structure theorem; Exercise Set Twelve; Exercise Set Thirteen 7. Consequences of the duality theoremExercise Set Fourteen; Exercise Set Fifteen; 8. Locally Euclidean and NSS-groups; Exercise Set Sixteen; 9. Non-abelian groups; References; Index of terms; Index of Exercises, propositions and theorems Locally compact Abelian groups. http://id.loc.gov/authorities/subjects/sh85077961 Duality theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85039851 Pontrjagin duality. http://id.loc.gov/authorities/subjects/sh2010014118 Abel, Groupes localement compacts d' Dualité, Théorie de la (Mathématiques) Groupes abéliens localement compacts. Principe de dualité (Mathématiques) Dualité de Pontrjagin. MATHEMATICS Algebra Linear. bisacsh Duality theory (Mathematics) fast Locally compact Abelian groups fast Pontrjagin duality fast Lokal kompakte Abelsche Gruppe gnd http://d-nb.info/gnd/4168093-5 Pontrjagin-Dualität gnd http://d-nb.info/gnd/4365532-4 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85077961 http://id.loc.gov/authorities/subjects/sh85039851 http://id.loc.gov/authorities/subjects/sh2010014118 http://d-nb.info/gnd/4168093-5 http://d-nb.info/gnd/4365532-4 |
| title | Pontryagin duality and the structure of locally compact abelian groups / |
| title_auth | Pontryagin duality and the structure of locally compact abelian groups / |
| title_exact_search | Pontryagin duality and the structure of locally compact abelian groups / |
| title_full | Pontryagin duality and the structure of locally compact abelian groups / Sidney A. Morris. |
| title_fullStr | Pontryagin duality and the structure of locally compact abelian groups / Sidney A. Morris. |
| title_full_unstemmed | Pontryagin duality and the structure of locally compact abelian groups / Sidney A. Morris. |
| title_short | Pontryagin duality and the structure of locally compact abelian groups / |
| title_sort | pontryagin duality and the structure of locally compact abelian groups |
| topic | Locally compact Abelian groups. http://id.loc.gov/authorities/subjects/sh85077961 Duality theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85039851 Pontrjagin duality. http://id.loc.gov/authorities/subjects/sh2010014118 Abel, Groupes localement compacts d' Dualité, Théorie de la (Mathématiques) Groupes abéliens localement compacts. Principe de dualité (Mathématiques) Dualité de Pontrjagin. MATHEMATICS Algebra Linear. bisacsh Duality theory (Mathematics) fast Locally compact Abelian groups fast Pontrjagin duality fast Lokal kompakte Abelsche Gruppe gnd http://d-nb.info/gnd/4168093-5 Pontrjagin-Dualität gnd http://d-nb.info/gnd/4365532-4 |
| topic_facet | Locally compact Abelian groups. Duality theory (Mathematics) Pontrjagin duality. Abel, Groupes localement compacts d' Dualité, Théorie de la (Mathématiques) Groupes abéliens localement compacts. Principe de dualité (Mathématiques) Dualité de Pontrjagin. MATHEMATICS Algebra Linear. Locally compact Abelian groups Pontrjagin duality Lokal kompakte Abelsche Gruppe Pontrjagin-Dualität |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552425 |
| work_keys_str_mv | AT morrissidneya pontryagindualityandthestructureoflocallycompactabeliangroups |