Introduction to metric and topological spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
1995
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| Edition: | Reprinted with corr. |
| Series: | Oxford science publications
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 181 S. graph. Darst. |
| ISBN: | 0198531613 |
Staff View
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Record in the Search Index
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| adam_text | W. A. SUTHERLAND INTRODUCTION TO METRIC AND TOPOLOGICAL SPACES CLARENDON
PRESS * OXFORD CONTENTS INTRODUCNON IX NOTATION AND TERMINOLOGY XI 1.
REVIEW OF SOME REAL ANALYSIS 1 1.1. REAL NUMBERS 1 1.2. REAL SEQUENCES 5
1.3. LIMITS OF FUNCTIONS 11 1.4. CONTINUITY 12 2. CONTINUITY
GENERALIZED: METRIC SPACES 19 2.1. MOTIVATION 19 2.2. EXATNPLES 22 2.3.
OPEN SETS IN METRIC SPACES 33 2.4. EQUIVALENT METRICS 38 2.5. CONTINUITY
42 3. CONTINUITY GENERALIZED: TOPOLOGICAL SPACES 45 3.1. TOPOLOGICAL
SPACES 45 3.2. BASES 49 3.3. SUB-BASES AND WEAK TOPOLOGIES 50 3.4.
SUBSPACES 51 3.5. PRODUCTS 53 3.6. HOMEOMORPHISMS 56 3.7. DEFINITIONS 59
3.8. QUOTIENT SPACES 65 4. THE HAUSDORFF CONDITION 72 4.1. MOTIVATION 72
4.2. SEPARATION AXIOMS 73 5. COMPACT SPACES 75 5.1. MOTIVATION 75 5.2.
DEFINITION OF COMPACTNESS 77 5.3. COMPACTNESS OF [A, B] 79 5.4.
PROPERTIES OF COMPACT SPACES 82 5.5. CONTINUOUS MAPS ON COMPACT SPACES
83 5.6. COMPACTNESS AND CONSTRUCTIONS 84 5.7. COMPACT SUBSPACES OF R 86
5.8. COMPACTNESS AND UNIFORM CONTINUITY 87 5.9. AN INVERSE FUNCTION
THEOREM 88 VIII CONTENTS 6. CONNECTED SPACES 93 6.1. INTRODUCTION 93
6.2. CONNECTEDNESS 93 6.3. PATH-CONNECTEDNESS 99 6.4. COMPARISON OF
DEFINITIONS 102 6.5. COMPONENTS 103 7. COMPACTNESS AGAIN: CONVERGENCE IN
METRIC SPACES 108 7.1. INTRODUCTION 108 7.2. SEQUENTIAL COMPACTNESS 108
8. UNIFORM CONVERGENCE 114 8.1. INTRODUCTION 114 8.2. DEFINITION AND
EXAMPLES 114 8.3. CAUCHY S CRITERION 119 8.4. UNIFORM LIMITS OF
SEQUENCES 120 8.5. GENERALIZATIONS 121 9. COMPLETE METRIC SPACES 123
9.1. INTRODUCTION 123 9.2. DEFINITION AND EXAMPLES 123 9.3. FIXED POINT
THEOREMS 129 9.4. THE CONTRACTION MAPPING THEOREM 130 9.5. CANTOR S AND
BAIRE S THEOREMS 133 10. CRITERIA FOR COMPACTNESS IN METRIC SPACES 139
10.1. A GENERAL CRITERION 139 10.2. ARZELAE-ASCOLI THEOREM 141 11.
APPENDIX 149 11.1. REAL NUMBERS 149 11.2. COMPLETION OF METRIC SPACES
155 12. GUIDE TO EXERCISES 160 BIBLIOGRAPHY 177 INDEX 179
|
| any_adam_object | 1 |
| author | Sutherland, W. A. |
| author_facet | Sutherland, W. A. |
| author_role | aut |
| author_sort | Sutherland, W. A. |
| author_variant | w a s wa was |
| building | Verbundindex |
| bvnumber | BV011496806 |
| classification_rvk | SK 280 |
| ctrlnum | (OCoLC)258231233 (DE-599)BVBBV011496806 |
| discipline | Mathematik |
| edition | Reprinted with corr. |
| format | Book |
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| isbn | 0198531613 |
| language | English |
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| physical | XIII, 181 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | Oxford Univ. Press |
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| spelling | Sutherland, W. A. Verfasser aut Introduction to metric and topological spaces W. A. Sutherland Reprinted with corr. Oxford [u.a.] Oxford Univ. Press 1995 XIII, 181 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford science publications Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Raum Mathematik (DE-588)4124030-3 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Hausdorff-Raum (DE-588)4159237-2 gnd rswk-swf Kompakter Raum (DE-588)4164857-2 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Metrischer Raum (DE-588)4169745-5 s Topologischer Raum (DE-588)4137586-5 s Kompakter Raum (DE-588)4164857-2 s Hausdorff-Raum (DE-588)4159237-2 s 2\p DE-604 Topologie (DE-588)4060425-1 s Raum Mathematik (DE-588)4124030-3 s 3\p DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007736965&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sutherland, W. A. Introduction to metric and topological spaces Metrischer Raum (DE-588)4169745-5 gnd Raum Mathematik (DE-588)4124030-3 gnd Topologie (DE-588)4060425-1 gnd Hausdorff-Raum (DE-588)4159237-2 gnd Kompakter Raum (DE-588)4164857-2 gnd Topologischer Raum (DE-588)4137586-5 gnd |
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| title | Introduction to metric and topological spaces |
| title_auth | Introduction to metric and topological spaces |
| title_exact_search | Introduction to metric and topological spaces |
| title_full | Introduction to metric and topological spaces W. A. Sutherland |
| title_fullStr | Introduction to metric and topological spaces W. A. Sutherland |
| title_full_unstemmed | Introduction to metric and topological spaces W. A. Sutherland |
| title_short | Introduction to metric and topological spaces |
| title_sort | introduction to metric and topological spaces |
| topic | Metrischer Raum (DE-588)4169745-5 gnd Raum Mathematik (DE-588)4124030-3 gnd Topologie (DE-588)4060425-1 gnd Hausdorff-Raum (DE-588)4159237-2 gnd Kompakter Raum (DE-588)4164857-2 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| topic_facet | Metrischer Raum Raum Mathematik Topologie Hausdorff-Raum Kompakter Raum Topologischer Raum Lehrbuch |
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