Locally compact groups: Markus Stroppel
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
Europ. Math. Soc.
2006
|
| Series: | EMS textbooks in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 302 S. graph. Darst. |
| ISBN: | 3037190167 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text |
Contents
Preface
v
A Preliminaries
1
1
Maps and Topologies
. 1
2
Connectedness and Topological Dimension
. 19
В
Topological Groups
26
3
Basic Definitions and Results
. 26
4
Subgroups
. 43
5
Linear Groups over Topological Rings
. 50
6
Quotients
. 53
7
Solvable and
Nilpotent
Groups
. 66
8
Completion
. 72
С
Topological Transformation Groups
91
9
The Compact-Open Topology
. 91
10
Transformation Groups
. 99
11
Sets, Groups, and Rings of Homomorphisms
. 105
D
The
Haar
Integral
113
12
Existence and Uniqueness of
Haar
Integrals
. 113
13
The Module Function
. 123
14
Applications to Linear Representations
. 128
E
Categories of Topological Groups
143
15
Categories
. 143
16
Products in Categories of Topological Groups
. 147
17
Direct Limits and
Projective
Limits
. 156
18
Projective
Limits of Topological Groups
. 165
19
Compact Groups
. 169
F
Locally Compact Abelian Groups
174
20
Characters and Character Groups
. 174
21
Compactly Generated Abelian Lie Groups
. 181
22
Pontryagin's Duality Theorem
. 191
23
Applications of the Duality Theorem
. 194
24
Maximal Compact Subgroups and Vector Subgroups
. 203
χ
Contents
25
Automorphism Groups of Locally Compact Abelian Groups
. . . 207
26
Locally Compact Rings and Fields
. 212
27
Homogeneous Locally Compact Groups
. 230
G
Locally Compact Semigroups
242
28
Topological Semigroups
. 242
29
Embedding Cancellative Directed Semigroups into Groups
. 250
30
Compact Semigroups
. 254
31
Groups with Continuous Multiplication
. 259
H
Hubert's Fifth Problem
261
32
The Approximation Theorem
. 261
33
Dimension of Locally Compact Groups
. 264
34
The Rough Structure
. 268
35
Notions of Simplicity
. 272
36
Compact Groups
. 276
37
Countable Bases, Metrizability
. 279
38
Non-Lie Groups of Finite Dimension
. 280
39
Arcwise Connected Subgroups
. 281
40
Algebraic Groups
. 285
Bibliography
287
Index of Symbols
291
Subject Index
297 |
| adam_txt |
Contents
Preface
v
A Preliminaries
1
1
Maps and Topologies
. 1
2
Connectedness and Topological Dimension
. 19
В
Topological Groups
26
3
Basic Definitions and Results
. 26
4
Subgroups
. 43
5
Linear Groups over Topological Rings
. 50
6
Quotients
. 53
7
Solvable and
Nilpotent
Groups
. 66
8
Completion
. 72
С
Topological Transformation Groups
91
9
The Compact-Open Topology
. 91
10
Transformation Groups
. 99
11
Sets, Groups, and Rings of Homomorphisms
. 105
D
The
Haar
Integral
113
12
Existence and Uniqueness of
Haar
Integrals
. 113
13
The Module Function
. 123
14
Applications to Linear Representations
. 128
E
Categories of Topological Groups
143
15
Categories
. 143
16
Products in Categories of Topological Groups
. 147
17
Direct Limits and
Projective
Limits
. 156
18
Projective
Limits of Topological Groups
. 165
19
Compact Groups
. 169
F
Locally Compact Abelian Groups
174
20
Characters and Character Groups
. 174
21
Compactly Generated Abelian Lie Groups
. 181
22
Pontryagin's Duality Theorem
. 191
23
Applications of the Duality Theorem
. 194
24
Maximal Compact Subgroups and Vector Subgroups
. 203
χ
Contents
25
Automorphism Groups of Locally Compact Abelian Groups
. . . 207
26
Locally Compact Rings and Fields
. 212
27
Homogeneous Locally Compact Groups
. 230
G
Locally Compact Semigroups
242
28
Topological Semigroups
. 242
29
Embedding Cancellative Directed Semigroups into Groups
. 250
30
Compact Semigroups
. 254
31
Groups with Continuous Multiplication
. 259
H
Hubert's Fifth Problem
261
32
The Approximation Theorem
. 261
33
Dimension of Locally Compact Groups
. 264
34
The Rough Structure
. 268
35
Notions of Simplicity
. 272
36
Compact Groups
. 276
37
Countable Bases, Metrizability
. 279
38
Non-Lie Groups of Finite Dimension
. 280
39
Arcwise Connected Subgroups
. 281
40
Algebraic Groups
. 285
Bibliography
287
Index of Symbols
291
Subject Index
297 |
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| id | DE-604.BV021579586 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:41:15Z |
| indexdate | 2025-03-06T15:01:19Z |
| institution | BVB |
| isbn | 3037190167 |
| language | English |
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| physical | X, 302 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Europ. Math. Soc. |
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| series2 | EMS textbooks in mathematics |
| spelling | Stroppel, Markus 1961- Verfasser (DE-588)112910831 aut Locally compact groups Markus Stroppel Zürich Europ. Math. Soc. 2006 X, 302 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier EMS textbooks in mathematics Groupes localement compacts Locally compact groups Lokal kompakte Gruppe (DE-588)4168094-7 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Lokal kompakte Gruppe (DE-588)4168094-7 s DE-604 Erscheint auch als Stroppel, Markus, 1961- Locally compact groups Online-Ausgabe 978-3-03719-516-1 (DE-604)BV036713211 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014795275&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stroppel, Markus 1961- Locally compact groups Markus Stroppel Groupes localement compacts Locally compact groups Lokal kompakte Gruppe (DE-588)4168094-7 gnd |
| subject_GND | (DE-588)4168094-7 (DE-588)4151278-9 |
| title | Locally compact groups Markus Stroppel |
| title_auth | Locally compact groups Markus Stroppel |
| title_exact_search | Locally compact groups Markus Stroppel |
| title_exact_search_txtP | Locally compact groups Markus Stroppel |
| title_full | Locally compact groups Markus Stroppel |
| title_fullStr | Locally compact groups Markus Stroppel |
| title_full_unstemmed | Locally compact groups Markus Stroppel |
| title_short | Locally compact groups |
| title_sort | locally compact groups markus stroppel |
| title_sub | Markus Stroppel |
| topic | Groupes localement compacts Locally compact groups Lokal kompakte Gruppe (DE-588)4168094-7 gnd |
| topic_facet | Groupes localement compacts Locally compact groups Lokal kompakte Gruppe Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014795275&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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