Topological groups: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XI, 367 S. |
| ISBN: | 9780470624517 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV036612402 | ||
| 003 | DE-604 | ||
| 005 | 20101111 | ||
| 007 | t | ||
| 008 | 100811s2010 xxu |||| 00||| eng d | ||
| 010 | |a 2010013147 | ||
| 020 | |a 9780470624517 |c cloth |9 978-0-470-62451-7 | ||
| 035 | |a (OCoLC)700522349 | ||
| 035 | |a (DE-599)BVBBV036612402 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-20 |a DE-19 |a DE-703 | ||
| 050 | 0 | |a QA387 | |
| 082 | 0 | |a 512/.55 | |
| 084 | |a SK 340 |0 (DE-625)143232: |2 rvk | ||
| 100 | 1 | |a Markley, Nelson Groh |d 1940- |e Verfasser |0 (DE-588)109072847 |4 aut | |
| 245 | 1 | 0 | |a Topological groups |b an introduction |c Nelson G. Markley |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2010 | |
| 300 | |a XI, 367 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Topological groups | |
| 650 | 0 | 7 | |a Topologische Gruppe |0 (DE-588)4135793-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Topologische Gruppe |0 (DE-588)4135793-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020532626&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020532626&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020532626 | ||
Datensatz im Suchindex
| _version_ | 1804143218677252096 |
|---|---|
| adam_text | Contents
Preface
ix
Groups and Topologies
1
1.1
Groups
................................. 2
1.2
Metric and Topological Spaces
................... 13
1.3
Continuous Group Operations
.................... 29
1.4
Subgroups and Their Quotient Spaces
............... 40
1.5
Compactness and Metric Groups
.................. 51
Linear Spaces and Algebras
63
2.1
Linear Structures on Groups
.................... 64
2.2
Linear Functions
........................... 70
2.3
Norms on Linear Spaces
....................... 83
2.4
Continuous Linear Functions
.................... 92
2.5
The Determinant Function
...................... 99
The Subgroups of W1
115
3.1
Closed Subgroups
...........................116
3.2
Quotient Groups
...........................125
3.3
Dense Subgroups
...........................132
Matrix Groups
140
4.1
General Linear Groups
........................141
4.2
Orthogonal and Unitary Groups
..................149
4.3
Triangular Groups
..........................159
4.4
One-Parameter Subgroups
......................169
Connectedness of Topological Groups
181
5.1
Connected Topological Spaces
....................182
5.2
Connected Matrix Groups
......................193
5.3
Compact Product Spaces
......................207
5.4
Totally Disconnected Groups
....................214
vii
viii CONTENTS
6
Metric
Groups of Functions
223
6.1
Real-Valued Functions
........................224
6.2
The Compact-Open Topology
....................233
6.3
Metric Groups of Isometries
.....................243
6.4
Metric Groups of Homeomorphisms
.................248
6.5
Metric Groups of Homomorphisms
.................255
7
Compact Groups
262
7.1
Invariant Means
...........................263
7.2
Integral Equations
..........................274
7.3
Eigenfunctions
............................292
7.4
Compact Abelian Groups
......................302
7.5
Matrix Representations
.......................310
8
Character Groups
319
8.1
Countable Discrete Abelian Groups
.................320
8.2
The Duality Homomorphism
....................329
8.3
Compactly Generated Abelian Groups
...............337
8.4
A Duality Theorem
..... .....................344
Bibliography
359
Index of Special Symbols
362
Index
364
чшіу
introduction
to metric
ar
Topological
Groups: An Introduction provides a self-contained presentation with an
emphasis on important families of topological groups. The book uniquely provides
a modern and balanced presentation by using metric groups to present a substantive
introduction to topics such as duality, while also shedding light on more general results
for topological groups.
Filling the need for a broad and accessible introduction to the subject, the book be¬
gins with coverage of groups, metric spaces, and topological spaces before introduc¬
ing topological groups. Since linear spaces, algebras, norms, and determinants are
necessary tools for studying topological groups, their basic properties are developed
in subsequent chapters. For concreteness, product topologies, quotient topologies, and
compact-open topologies are first introduced as metric spaces before their open sets are
characterized by topological properties. These metrics, along with invariant metrics,
act as excellent stepping stones to the subsequent discussions of the following topics:
•
Matrix groups
s Connectednesss of topological groups
•
Compact groups
Character groups
Exercises found throughout the book are designed so both novice and advanced read¬
ers will be able to work out solutions and move forward at their desired pace. All
chapters include a variety of calculations, remarks, and elementary results, which are
incorporated into the various examples and exercises.
Topologicul
Groups: An Introduction is an excellent book for advanced undergraduate
and graduate-level courses on the topic. The book also serves as a valuable resource for
professionals working in the fields of mathematics, science, engineering, and physics.
was professor of mathematics at the University of
Maryland for more than twenty-five years and also served as provost at Lehigh Univer¬
sity. He has written numerous journal articles in the area of dynamical systems and is
the author of
Principies
of Differential Equations, also published by Wiley.
Ψ
WILEY
wiiev.com
ISBN
476-0-470^5451-7
90000
9
780470ll624517l
|
| any_adam_object | 1 |
| author | Markley, Nelson Groh 1940- |
| author_GND | (DE-588)109072847 |
| author_facet | Markley, Nelson Groh 1940- |
| author_role | aut |
| author_sort | Markley, Nelson Groh 1940- |
| author_variant | n g m ng ngm |
| building | Verbundindex |
| bvnumber | BV036612402 |
| callnumber-first | Q - Science |
| callnumber-label | QA387 |
| callnumber-raw | QA387 |
| callnumber-search | QA387 |
| callnumber-sort | QA 3387 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 340 |
| ctrlnum | (OCoLC)700522349 (DE-599)BVBBV036612402 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01632nam a2200397zc 4500</leader><controlfield tag="001">BV036612402</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20101111 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">100811s2010 xxu |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2010013147</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780470624517</subfield><subfield code="c">cloth</subfield><subfield code="9">978-0-470-62451-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)700522349</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV036612402</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-703</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA387</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.55</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 340</subfield><subfield code="0">(DE-625)143232:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Markley, Nelson Groh</subfield><subfield code="d">1940-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)109072847</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Topological groups</subfield><subfield code="b">an introduction</subfield><subfield code="c">Nelson G. Markley</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Hoboken, NJ</subfield><subfield code="b">Wiley</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 367 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="650" ind1=" " ind2="4"><subfield code="a">Topological groups</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Topologische Gruppe</subfield><subfield code="0">(DE-588)4135793-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Topologische Gruppe</subfield><subfield code="0">(DE-588)4135793-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</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=020532626&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</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=020532626&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Klappentext</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-020532626</subfield></datafield></record></collection> |
| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV036612402 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:44:10Z |
| institution | BVB |
| isbn | 9780470624517 |
| language | English |
| lccn | 2010013147 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020532626 |
| oclc_num | 700522349 |
| open_access_boolean | |
| owner | DE-20 DE-19 DE-BY-UBM DE-703 |
| owner_facet | DE-20 DE-19 DE-BY-UBM DE-703 |
| physical | XI, 367 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Wiley |
| record_format | marc |
| spelling | Markley, Nelson Groh 1940- Verfasser (DE-588)109072847 aut Topological groups an introduction Nelson G. Markley Hoboken, NJ Wiley 2010 XI, 367 S. txt rdacontent n rdamedia nc rdacarrier Topological groups Topologische Gruppe (DE-588)4135793-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Topologische Gruppe (DE-588)4135793-0 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020532626&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020532626&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Markley, Nelson Groh 1940- Topological groups an introduction Topological groups Topologische Gruppe (DE-588)4135793-0 gnd |
| subject_GND | (DE-588)4135793-0 (DE-588)4123623-3 |
| title | Topological groups an introduction |
| title_auth | Topological groups an introduction |
| title_exact_search | Topological groups an introduction |
| title_full | Topological groups an introduction Nelson G. Markley |
| title_fullStr | Topological groups an introduction Nelson G. Markley |
| title_full_unstemmed | Topological groups an introduction Nelson G. Markley |
| title_short | Topological groups |
| title_sort | topological groups an introduction |
| title_sub | an introduction |
| topic | Topological groups Topologische Gruppe (DE-588)4135793-0 gnd |
| topic_facet | Topological groups Topologische Gruppe Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020532626&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020532626&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT markleynelsongroh topologicalgroupsanintroduction |