Elements of abstract analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2002
|
| Series: | Springer undergraduate mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 298 S. |
| ISBN: | 185233424X |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
MICHEAL 0 SEARCOID
ELEMENTS OF ABSTRACT
ANALYSIS
SPRINGER
IMAGE 2
CONTENTS
LET US FROM POINT TO POINT THIS STORY KNOW, TO MAKE THE EVEN TRUTH IN
PLEASURE FLOW. ALL S WELL THAT ENDS WELL, V.III.
LIST OF SYMBOLS XI
1. SETS 1
1.1 SET THEORY 2
1.2 RELATIONS AND FUNCTIONS 12
1.3 ORDERED SETS 20
1.4 ORDINALS 29
1.5 THE AXIOM OF CHOICE 35
2. COUNTING 41
2.1 COUNTING NUMBERS 41
2.2 CARDINALITY 44
2.3 ENUMERATION 47
2.4 CARDINALITY OF UNIONS AND PRODUCTS 53
3. ALGEBRAIC STRUCTURE 57
3.1 ELEMENTARY ALGEBRAIC STRUCTURES 57
3.2 VECTOR SPACES 69
3.3 ALGEBRAS 77
3.4 PRESERVATION OF ALGEBRAIC STRUCTURE 80
4. ANALYTIC STRUCTURE 91
4.1 ORDERED ALGEBRAIC STRUCTURE 91
4.2 NUMBER SYSTEMS . : 96
4.3 REAL AND COMPLEX FUNCTIONS 102
4.4 INEQUALITIES 112
IX
IMAGE 3
ELEMENTS OF ABSTRACT ANALYSIS
5. LINEAR STRUCTURE 115
5.1 LINEAR SPACES AND ALGEBRAS 115
5.2 LINEAR SHAPES 118
5.3 LINEAR FUNCTIONAL 129
6. GEOMETRIC STRUCTURE 133
6.1 SEMIMETRICS AND METRICS 133
6.2 SEMINORMS AND NORMS 142
6.3 SESQUILINEAR FORMS AND INNER PRODUCTS 156
7. TOPOLOGICAL STRUCTURE 159
7.1 TOPOLOGIES 159
7.2 NEIGHBOURHOODS 165
7.3 CARDINALITY AND TOPOLOGY 172
7.4 SEPARATION 175
8. CONTINUITY AND OPENNESS 177
8.1 PRESERVATION OF TOPOLOGICAL STRUCTURE 177
8.2 TOPOLOGIES DEFINED BY FUNCTIONS 187
8.3 DERIVED TOPOLOGICAL SPACES 191
8.4 TOPOLOGIES ON LINEAR SPACES 202
9. CONNECTEDNESS 207
9.1 CONNECTED SPACES 207
9.2 PATHWISE CONNECTEDNESS 213
10. CONVERGENCE 215
10.1 FILTERS 215
10.2 LIMITS 221
11. COMPACTNESS 231
11.1 COMPACT TOPOLOGICAL SPACES 231
11.2 COMPACT HAUSDORFF SPACES 238
11.3 LOCAL COMPACTNESS 243
12. COMPLETENESS 245
12.1 COMPLETE METRIC SPACES 245
12.2 BANACH SPACES 254
12.3 HILBERT SPACES 258
12.4 BANACH ALGEBRAS 262
SOLUTIONS 269
BIBLIOGRAPHY 285
INDEX 287
|
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T18:52:12Z |
| institution | BVB |
| isbn | 185233424X |
| language | English |
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| physical | XII, 298 S. |
| publishDate | 2002 |
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| publisher | Springer |
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| series2 | Springer undergraduate mathematics series |
| spelling | Ó Searcóid, Mícheál 1948- Verfasser (DE-588)122982827 aut Elements of abstract analysis Mícheál Ó Searcóid London [u.a.] Springer 2002 XII, 298 S. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Analyse fonctionnelle Functional analysis Analysis (DE-588)4001865-9 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 Funktionalanalysis (DE-588)4018916-8 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009434957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ó Searcóid, Mícheál 1948- Elements of abstract analysis Analyse fonctionnelle Functional analysis Analysis (DE-588)4001865-9 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4018916-8 |
| title | Elements of abstract analysis |
| title_auth | Elements of abstract analysis |
| title_exact_search | Elements of abstract analysis |
| title_full | Elements of abstract analysis Mícheál Ó Searcóid |
| title_fullStr | Elements of abstract analysis Mícheál Ó Searcóid |
| title_full_unstemmed | Elements of abstract analysis Mícheál Ó Searcóid |
| title_short | Elements of abstract analysis |
| title_sort | elements of abstract analysis |
| topic | Analyse fonctionnelle Functional analysis Analysis (DE-588)4001865-9 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Analyse fonctionnelle Functional analysis Analysis Funktionalanalysis |
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