Fundamentals of topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Macmillan u.a.
1976
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 179 S. graph.Darst. |
| ISBN: | 0024106402 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Chapter 0. Introduction 1
0 1 Logic 1
0 2 Sets, Relations, and Functions 2
0 3 Orderings, Lattices, and Chains 8
0 4 Equivalents of the Axiom of Choice 11
*0 5 Groups, Homomorphisms, and Isomorphisms 13
Chapter 1. Topological Spaces 17
1 1 Topologies 17
1 2 Bases and Subbases 20
1 3 Limit Points, Boundary Points, and Sequential Limits 23
1 4 Continuity, Homeomorphisms, and Topological
Properties 25
1 5 Subspaces and Product Spaces 28
1 6 Separable Spaces 31
1 7 First and Second Countable Spaces 32
1 8 Distance, Uniform, and Proximity Spaces 34
*l 9 Function Spaces and Quotient Spaces 39
Chapter 2. The Separation Axioms 45
2 1 To, Tu T2, and T5n 45
2 2 Regular (T3) and Completely Regular (T1/2) 49
2 3 Normal (T4) and Completely Normal (Ts) 52
*2 4 CoIIectionwise Normal 58
Chapter 3. Covering Properties 59
3 1 Compactness 59
3 2 Lindelof Spaces 64
3 3 Countable Compactness 66
3 4 Sequential Compactness 69
3 5 Bolzano Weierstrass Property 72
*3 6 Developable Spaces 75
*3 7 Paracompactness 78
*3 8 Compactification 82
Chapter 4. Connectivity Properties 85
4 1 Connectivity 85
4 2 Components and Continua 89
4 3 Local Connectivity 92
*4 4 Pathwise Connectivity 95
*4~5 Arcwise Connectivity 99
ix
x Contents
Chapter 5. Metrization 101
5 1 Metrizability 101
*5 2 Semimetrizable and a Metrizable Spaces 106
•5 3 Uniform Spaces 109
¦^5 4 Topological Groups 112
Chapter 6. Convergence and Completeness 115
6 1 Sequences and Filters 115
6 2 Completeness 119
¦* 6 3 Completions of Metric and Uniform Spaces 123
¦^6 4 Applications of Completeness 125
Chapter 7. Homotopy Theory 129
7 1 Retracts 129
7 2 Homotopic Mappings 130
7 3 Contractible and Starlike Spaces 132
7 4 Homotopically Equivalent Spaces 134
7 5 The Fundamental Group 135
*7 6 The Higher Homotopy Groups 141
Chapter 8. Singular Homology Theory 143
8 1 Simplexes and Complexes 143
8 2 Singular Chains 146
8 3 Singular Homology Groups 149
8 4 Properties of Singular Homology 151
8 5 The Homology Sequence 155
8 6 Homology of Cells and Spheres 160
8 7 Applications of Homotopy and Homology 162
Bibliography 169
Index 175
|
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| id | DE-604.BV001988273 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:27Z |
| institution | BVB |
| isbn | 0024106402 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001296858 |
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| publishDate | 1976 |
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| spelling | Sims, Benjamin T. Verfasser aut Fundamentals of topology New York u.a. Macmillan u.a. 1976 X, 179 S. graph.Darst. txt rdacontent n rdamedia nc rdacarrier Topology HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001296858&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sims, Benjamin T. Fundamentals of topology Topology |
| title | Fundamentals of topology |
| title_auth | Fundamentals of topology |
| title_exact_search | Fundamentals of topology |
| title_full | Fundamentals of topology |
| title_fullStr | Fundamentals of topology |
| title_full_unstemmed | Fundamentals of topology |
| title_short | Fundamentals of topology |
| title_sort | fundamentals of topology |
| topic | Topology |
| topic_facet | Topology |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001296858&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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