Topologies and uniformities:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
1999
|
| Series: | Springer undergraduate mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Exp. and rev. version of: Topological and uniform spaces |
| Physical Description: | XV, 230 S. graph. Darst. |
| ISBN: | 1852330619 |
Staff View
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Record in the Search Index
| _version_ | 1825094773432647680 |
|---|---|
| adam_text |
Contents
Introduction ix
Historical Note xiii
Chapter 1 Topological Spaces 1
1.1 General remarks 1
1.2 Direct and inverse images 2
1.3 Cartesian products 3
1.4 Relations 4
1.5 Axioms of topology 5
1.6 Closure and interior 8
1.7 Generating families 11
1.8 Ordered sets 12
1.9 Filters 14
1.10 Neighbourhoods 17
1.11 Metric spaces 19
1.12 Filters on topological spaces 23
Exercises 26
Chapter 2 Continuity 29
2.1 General remarks 29
2.2 Continuous functions 30
2.3 Homeomorphisms 34
2.4 The topological product 35
2.5 Topological groups 42
Exercises 45
v
vi Topologies and Uniformities
Chapter 3 The Induced Topology and Its Dual 47
3.1 The induced topology 47
3.2 Subspaces 51
3.3 The coinduced topology 56
3.4 Quotient spaces 58
Exercises 60
Chapter 4 Open Functions and Closed Functions 63
4.1 General remarks 63
4.2 Open functions 63
4.3 Closed functions 67
Exercises 72
Chapter 5 Compact Spaces 75
5.1 Introduction 75
5.2 Compactness via filters 79
5.3 Compactness via coverings 83
Exercises 85
Chapter 6 Separation Conditions 87
6.1 General remarks 87
6.2 Ti spaces 87
6.3 Hausdorff spaces 88
6.4 Regular spaces 94
6.5 Normal spaces 97
6.6 Compactly regular spaces 100
Exercises 102
Chapter 7 Uniform Spaces 103
7.1 Uniform structures 103
7.2 Separated uniformities 108
7.3 Totally bounded uniformities 108
7.4 Uniform continuity 110
7.5 Uniform equivalences 112
7.6 The uniform product 113
7.7 The induced uniformity 115
7.8 The coinduced uniformity? 120
Exercises 124
Chapter 8 The Uniform Topology 127
8.1 Uniform neighbourhoods 127
Contents vii
8.2 Closure in uniform spaces 131
8.3 Uniformization of compact Hausdorff spaces 134
8.4 Cauchy sequences 136
8.5 Cauchy filters 138
8.6 Uniformization of function spaces 141
Exercises 144
Chapter 9 Connectedness 145
9.1 Connected spaces 145
9.2 Connectedness components 150
9.3 Locally connected spaces 152
9.4 Pathwise connected spaces 152
9.5 Uniformly connected spaces 159
9.6 Uniformly locally connected spaces 161
Exercises 163
Chapter 10 Countability and Related Topics 165
10.1 Countability 165
10.2 Lindelof spaces 166
10.3 Countably compact spaces 168
10.4 Sequentially compact spaces 170
10.5 Separable spaces 173
Exercises 176
Chapter 11 Functional Separation Conditions 179
11.1 General remarks 179
11.2 Completely regular spaces 179
11.3 Uniformizability 181
11.4 The Urysohn theorem 183
11.5 The Tietze theorem 185
Exercises 187
Chapter 12 Completeness and Completion 189
12.1 Complete uniform spaces 189
12.2 Metric completion 197
12.3 Uniform completion 199
Exercises 200
Select Bibliography 203
Solutions to Exercises 205
Index 227 |
| any_adam_object | 1 |
| author | James, Ioan M. 1928-2025 |
| author_GND | (DE-588)119539888 |
| author_facet | James, Ioan M. 1928-2025 |
| author_role | aut |
| author_sort | James, Ioan M. 1928-2025 |
| author_variant | i m j im imj |
| building | Verbundindex |
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| ctrlnum | (OCoLC)468556961 (DE-599)BVBBV012429813 |
| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| spelling | James, Ioan M. 1928-2025 Verfasser (DE-588)119539888 aut Topologies and uniformities Ioan James London [u.a.] Springer 1999 XV, 230 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Exp. and rev. version of: Topological and uniform spaces Topologie ram Uniformer Raum (DE-588)4137585-3 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Topologischer Raum (DE-588)4137586-5 s DE-604 Uniformer Raum (DE-588)4137585-3 s Topologie (DE-588)4060425-1 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008435041&sequence=000002&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 |
| spellingShingle | James, Ioan M. 1928-2025 Topologies and uniformities Topologie ram Uniformer Raum (DE-588)4137585-3 gnd Topologischer Raum (DE-588)4137586-5 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4137585-3 (DE-588)4137586-5 (DE-588)4060425-1 (DE-588)4151278-9 |
| title | Topologies and uniformities |
| title_auth | Topologies and uniformities |
| title_exact_search | Topologies and uniformities |
| title_full | Topologies and uniformities Ioan James |
| title_fullStr | Topologies and uniformities Ioan James |
| title_full_unstemmed | Topologies and uniformities Ioan James |
| title_short | Topologies and uniformities |
| title_sort | topologies and uniformities |
| topic | Topologie ram Uniformer Raum (DE-588)4137585-3 gnd Topologischer Raum (DE-588)4137586-5 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topologie Uniformer Raum Topologischer Raum Einführung |
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