Foundations of topology:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boston
PWS Publ.
1993
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017451635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 349 S. graph. Darst. |
| ISBN: | 0534932649 |
Internformat
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Datensatz im Suchindex
| _version_ | 1819309853521215488 |
|---|---|
| adam_text | Contents
^9 Topological Spaces 1
1 Metric Spaces 1
2 Topological Spaces: The Definition and Examples 10
3 Basis for a Topology 15
4 Closed Sets, Closures, and Interiors of Sets 26
5 Metric Spaces Revisited 36
6 Convergence 42
7 Continuous Functions and Homeomorphisms 50
^9 New Spaces from Old Ones 59
1 Subspaces 59
2 The Product Topology on X x Y 67
3 The Product Topology 73
4 The Weak Topology and the Product Topology 80
5 The Uniform Metric 85
6 Quotient Spaces 90
^9 Connectedness 102
1 Connected Spaces 102
2 Path wise and Local Connectedness 112
3 Totally Disconnected Spaces 119
^^M Compactness 123
1 Compactness in Metric Spaces 123
2 Compact Spaces 131
xiii
Contents
3 Local Compactness and the Relation Between Various Forms of
Compactness 140
4 The Weak Topology on a Topological Space 145
5 Equicontinuity 149
The Separation and Countability Axioms 154
1 To-, Ti-, and T2-Spaces 154
2 Regular and Completely Regular Spaces 159
3 Normal and Completely Normal Spaces 167
4 The Countability Axioms 172
5 Urysohn s Lemma and the Tietze Extension Theorem 176
6 Embeddings 180
Special Topics 185
1 Contraction Mappings in Metric Spaces 185
2 Normed Linear Spaces 187
3 The Frechet Derivative 192
4 Manifolds 199
5 Fractals 210
6 Compactifications 218
7 The Alexander Subbase and the Tychonoff Theorems 225
Metrizability and Paracompactness 229
1 Urysohn s Metrization Theorem 229
2 Paracompactness 232
3 The Nagata-Smirnov Metrization Theorem 241
I The Fundamental Group and Covering Spaces 248
1 Homotopy of Paths 248
2 The Fundamental Group 257
3 The Fundamental Group of the Circle 261
4 Covering Spaces 265
5 Applications and Additional Examples of Fundamental Groups 268
6 Knots 274
II Applications of Homotopy 281
1 Inessential Maps 281
2 The Fundamental Theorem of Algebra 283
Contents xv
3 Homotopic Maps 285
4 The Jordan Curve Theorem 287
A Logic and Proofs 294
B Sets 300
C Functions 305
D Indexing Sets and Cartesian Products 311
E Equivalence Relations and Order Relations 315
F Countable Sets 320
G Uncountable Sets 324
H Ordinal and Cardinal Numbers 326
I Algebra 331
Bibliography 338
Index 340
|
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| id | DE-604.BV023809466 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:34:37Z |
| institution | BVB |
| isbn | 0534932649 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017451635 |
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| physical | XV, 349 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | PWS Publ. |
| record_format | marc |
| spellingShingle | Patty, C. Wayne Foundations of topology Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 |
| title | Foundations of topology |
| title_auth | Foundations of topology |
| title_exact_search | Foundations of topology |
| title_full | Foundations of topology C. Wayne Patty |
| title_fullStr | Foundations of topology C. Wayne Patty |
| title_full_unstemmed | Foundations of topology C. Wayne Patty |
| title_short | Foundations of topology |
| title_sort | foundations of topology |
| topic | Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017451635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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