Introduction to metric and topological spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2009
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [201] |
| Beschreibung: | XI, 206 S. Ill. graph. Darst. |
| ISBN: | 9780199563074 9780199563081 0199563071 019956308X |
Internformat
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Datensatz im Suchindex
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| adam_text | Titel: Introduction to metric and topological spaces
Autor: Sutherland, Wilson A.
Jahr: 2009
Contents
1. Introduction 1
2. Notation and terminology 5
3. More on sets and functions 9
Direct and inverse images 9
Inverse functions 13
4. Review of some real analysis 17
Real numbers 17
Real sequences 20
Limits of functions 25
Continuity 27
Examples of continuous functions 30
5. Metric spaces 37
Motivation and definition 37
Examples of metric spaces 40
Results about continuous functions on metric spaces 48
Bounded sets in metric spaces 50
Open balls in metric spaces 51
Open sets in metric spaces 53
6. More concepts in metric spaces 61
Closed sets 61
Closure 62
Limit points 64
Interior 65
Boundary 67
Convergence in metric spaces 68
Equivalent metrics 69
Review 72
7. Topological spaces 77
Definition 77
Examples 78
X Contents
8. Continuity in topological spaces; bases 83
Definition 83
Homeomorphisms 84
Bases 85
9. Some concepts in topological spaces 89
10. Subspaces and product spaces 97
Subspaces 97
Products 99
Graphs 104
Postscript on products 105
11. The Hausdorff condition 109
Motivation 109
Separation conditions 110
12. Connected spaces 113
Motivation 113
Connectedness 113
Path-connectedness 119
Comparison of definitions 120
Connectedness and homeomorphisms 122
13. Compact spaces 125
Motivation 125
Definition of compactness 127
Compactness of closed bounded intervals 129
Properties of compact spaces 129
Continuous maps on compact spaces 131
Compactness of subspaces and products 132
Compact subsets of Euclidean spaces 134
Compactness and uniform continuity 135
An inverse function theorem 135
14. Sequential compactness 141
Sequential compactness for real numbers 141
Sequential compactness for metric spaces 142
15. Quotient spaces and surfaces 151
Motivation 151
A formal approach 153
The quotient topology 155
Main property of quotients 157
Contents xi
The circle 158
The torus 159
The real projective plane and the Klein bottle 160
Cutting and pasting 167
The shape of things to come 168
16. Uniform convergence 173
Motivation 173
Definition and examples 173
Cauchy s criterion 177
Uniform limits of sequences 178
Generalizations 180
17. Complete metric spaces 183
Definition and examples 184
Banach s fixed point theorem 190
Contraction mappings 192
Applications of Banach s fixed point theorem 193
Bibliography 201
Index 203
|
| any_adam_object | 1 |
| author | Sutherland, Wilson A. |
| author_facet | Sutherland, Wilson A. |
| author_role | aut |
| author_sort | Sutherland, Wilson A. |
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| classification_rvk | SK 280 |
| ctrlnum | (OCoLC)318670561 (DE-599)OBVAC07680668 |
| dewey-full | 514.32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.32 |
| dewey-search | 514.32 |
| dewey-sort | 3514.32 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T21:43:04Z |
| institution | BVB |
| isbn | 9780199563074 9780199563081 0199563071 019956308X |
| language | English |
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| physical | XI, 206 S. Ill. graph. Darst. |
| publishDate | 2009 |
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| spelling | Sutherland, Wilson A. Verfasser aut Introduction to metric and topological spaces Wilson A. Sutherland 2. ed. Oxford Oxford Univ. Press 2009 XI, 206 S. Ill. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [201] Topological spaces Metric spaces Topologie (DE-588)4060425-1 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Kompakter Raum (DE-588)4164857-2 gnd rswk-swf Hausdorff-Raum (DE-588)4159237-2 gnd rswk-swf Raum Mathematik (DE-588)4124030-3 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Topologie (DE-588)4060425-1 s Raum Mathematik (DE-588)4124030-3 s DE-604 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 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017730614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sutherland, Wilson A. Introduction to metric and topological spaces Topological spaces Metric spaces Topologie (DE-588)4060425-1 gnd Topologischer Raum (DE-588)4137586-5 gnd Kompakter Raum (DE-588)4164857-2 gnd Hausdorff-Raum (DE-588)4159237-2 gnd Raum Mathematik (DE-588)4124030-3 gnd Metrischer Raum (DE-588)4169745-5 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 Wilson A. Sutherland |
| title_fullStr | Introduction to metric and topological spaces Wilson A. Sutherland |
| title_full_unstemmed | Introduction to metric and topological spaces Wilson A. Sutherland |
| title_short | Introduction to metric and topological spaces |
| title_sort | introduction to metric and topological spaces |
| topic | Topological spaces Metric spaces Topologie (DE-588)4060425-1 gnd Topologischer Raum (DE-588)4137586-5 gnd Kompakter Raum (DE-588)4164857-2 gnd Hausdorff-Raum (DE-588)4159237-2 gnd Raum Mathematik (DE-588)4124030-3 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| topic_facet | Topological spaces Metric spaces Topologie Topologischer Raum Kompakter Raum Hausdorff-Raum Raum Mathematik Metrischer Raum Lehrbuch |
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