Principles of topology
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia u.a.
Saunders College Publ.
1989
|
| Schriftenreihe: | The Saunders series
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Principles of topology |c Fred H. Croom |
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| 300 | |a XI, 312 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1819639093389164544 |
|---|---|
| adam_text | PRINCIPLES
OF TOPOLOGY
Fred H Croom
The University of the South
CONTENTS
PREFACE
CHAPTER 1 Introduction 1
1 1 The Nature of Topology 1
1 2 The Origin of Topology 7
1 3 Preliminary Ideas from Set Theory 11
1 4 Operations on Sets: Union, Intersection, and Difference • 14
1 5 Cartesian Products 19
1 6 Functions 20
1 7 Equivalence Relations 25
CHAPTER 2 The Line and the Plane 29
2 1 Upper and Lower Bounds 29
2 2 Finite and Infinite Sets 33
2 3 Open Sets and Closed Sets on the Real Line 39
2 4 The Nested Intervals Theorem 46
2 5 The Plane 49
Suggestions for Further Reading 51
Historical Notes for Chapter 2 53
CHAPTER 3 Metric Spaces 55
3 1 The Definition and Some Examples 55
3 2 Open Sets and Closed Sets in Metric Spaces 61
3 3 Interior, Closure, and Boundary 69
3 4 Continuous Functions 75
3 5 Equivalence of Metric Spaces 78
3 6 New Spaces from Old 82
3 7 Complete Metric Spaces 87
Suggestions for Further Reading 96
Historical Notes for Chapter 3 97
IX
X CONTENTS
CHAPTER 4 Topological Spaces 99
4 1 The Definition and Some Examples 99
4 2 Interior, Closure, and Boundary 103
4 3 Basis and Subbasis 109
4 4 Continuity and Topological Equivalence 115
4 5 Subspaces 122
Suggestions for Further Reading 128
Historical Notes for Chapter 4 129
CHAPTER 5 Connectedness 131
5 1 Connected and Disconnected Spaces 131
5 2 Theorems on Connectedness 133
5 3 Connected Subsets of the Real Line 143
5 4 Applications of Connectedness 144
5 5 Path Connected Spaces 147
5 6 Locally Connected and Locally Path Connected Spaces 154
Suggestions for Further Reading 159
Historical Notes for Chapter 5 160
CHAPTER 6 Compactness 161
6 1 Compact Spaces and Subspaces 161
6 2 Compactness and Continuity 167
6 3 Properties Related to Compactness 172
6 4 One-Point Compactification 181
6 5 The Cantor Set 187
Suggestions for Further Reading 192
Historical Notes for Chapter 6 193
CHAPTER 7 Product and Quotient Spaces 195
7 1 Finite Products 195
7 2 Arbitrary Products 204
7 3 Comparison of Topologies 211
7 4 Quotient Spaces 213
7 5 Surfaces and Manifolds 221
Suggestions for Further Reading 228
Historical Notes for Chapter 7 229
CONTENTS xi
CHAPTER 8 Separation Properties and
Metrization 231
8 1 To, T,, andT2-Spaces 231
8 2 Regular Spaces 234
8 3 Normal Spaces 237
8 4 Separation by Continuous Functions 243
8 5 Metrization 253
8 6 The Stone-Cech Compactification 261
Suggestions for Further Reading 265
Historical Notes for Chapter 8 266
CHAPTER 9 The Fundamental Group 267
9 1 The Nature of Algebraic Topology 267
9 2 The Fundamental Group 267
9 3 The Fundamental Group of S1 280
9 4 Additional Examples of Fundamental Groups 286
9 5 The Brouwer Fixed Point Theorem and Related Results 291
9 6 Categories and Functors 295
Suggestions for Further Reading 298
Historical Notes for Chapter 9 299
APPENDIX: Introduction to Groups 301
BIBLIOGRAPHY 303
INDEX 305
|
| any_adam_object | 1 |
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| 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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| id | DE-604.BV004549279 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T11:18:46Z |
| institution | BVB |
| isbn | 0030128137 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002799232 |
| oclc_num | 18497171 |
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| owner | DE-91 DE-BY-TUM DE-703 DE-739 |
| owner_facet | DE-91 DE-BY-TUM DE-703 DE-739 |
| physical | XI, 312 S. graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Saunders College Publ. |
| record_format | marc |
| series2 | The Saunders series |
| spellingShingle | Croom, Fred H. Principles of topology Topologie gtt Topology Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 |
| title | Principles of topology |
| title_auth | Principles of topology |
| title_exact_search | Principles of topology |
| title_full | Principles of topology Fred H. Croom |
| title_fullStr | Principles of topology Fred H. Croom |
| title_full_unstemmed | Principles of topology Fred H. Croom |
| title_short | Principles of topology |
| title_sort | principles of topology |
| topic | Topologie gtt Topology Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topologie Topology |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002799232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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