A guide to topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Washington, DC
Math. Assoc. of America
2009
|
| Series: | Dolciani mathematical expositions
40 MAA guides 4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 107 S. graph. Darst. |
| ISBN: | 9780883853467 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
.........................................................
vii
1
Fundamentals
............................................... 1
1.1
What is Topology?
...................... 1
1.2
First Definitions
....................... 1
1.3
Mappings
.......................... 8
1.4
The Separation Axioms
................... 11
1.5
Compactness
......................... 17
1.6
Homeomorphisms
...................... 21
1.7
Connectedness
........................ 24
1.8
Path-Connectedness
..................... 27
1.9
Continua
........................... 28
1.10
Totally Disconnected Spaces
................ 30
1.11
The Cantor Set
........................ 33
1.12
Metric Spaces
........................ 36
1.13
Metrizability
......................... 40
1.14
Baire s Theorem
....................... 41
1.15
Lebesgue s Lemma and Lebesgue Numbers
........ 45
2
Advanced Properties of Topological Spaces
................... 47
2.1
Basis and Subbasis
..................... 47
2.2
Product Spaces
........................ 48
2.3
Relative Topology
...................... 51
2.4
First Countable and Second Countable
........... 51
2.5
Compactifications
...................... 54
2.6
Quotient Topologies
..................... 56
2.7
Uniformities
......................... 58
2.8
Morse Theory
........................ 60
2.9
Proper Mappings
...................... 65
2.10
Paracompactness
....................... 66
XII CONTENTS
3 Moore-Smith
Convergence
and Nets
.......................... 69
3.1
Introductory Remarks
.................... 69
3.2
Nets
............................. 69
4
Function Spaces
............................................. 73
4.1
Preliminary Ideas
...................... 73
4.2
The Topology of Pointwise Convergence
.......... 74
4.3
The Compact-Open Topology
................ 75
4.4
Uniform Convergence
.................... 76
4.5
Equicontinuity and the Ascoli-Arzela Theorem
....... 78
4.6
The
Weierstrass
Approximation Theorem
.......... 81
Table of Notation
............................................... 87
Glossary
........................................................ 91
Bibliography
................................................... 99
Index
...........................................................103
About the Author
...............................................107
|
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| indexdate | 2024-07-09T22:03:41Z |
| institution | BVB |
| isbn | 9780883853467 |
| language | English |
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| physical | XII, 107 S. graph. Darst. |
| publishDate | 2009 |
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| publisher | Math. Assoc. of America |
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| series | Dolciani mathematical expositions MAA guides |
| series2 | Dolciani mathematical expositions MAA guides |
| spelling | Krantz, Steven G. 1951- Verfasser (DE-588)130535907 aut A guide to topology Steven G. Krantz Washington, DC Math. Assoc. of America 2009 XII, 107 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dolciani mathematical expositions 40 MAA guides 4 Topology Topologie (DE-588)4060425-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Topologie (DE-588)4060425-1 s DE-604 Dolciani mathematical expositions 40 (DE-604)BV001900740 40 MAA guides 4 (DE-604)BV035218151 4 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018612230&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4060425-1 (DE-588)4123623-3 |
| title | A guide to topology |
| title_auth | A guide to topology |
| title_exact_search | A guide to topology |
| title_full | A guide to topology Steven G. Krantz |
| title_fullStr | A guide to topology Steven G. Krantz |
| title_full_unstemmed | A guide to topology Steven G. Krantz |
| title_short | A guide to topology |
| title_sort | a guide to topology |
| topic | Topology Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topology Topologie Lehrbuch |
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