Introductory topology: exercises and solutions
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai
World Scientific
[2017]
|
| Ausgabe: | Second edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xvii, 356 Seiten |
| ISBN: | 9789813146938 9789813148024 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introductory topology |b exercises and solutions |c Mohammed Hichem Mortad (University of Oran 1, Ahmed Ben Bella, Algeria) |
| 250 | |a Second edition | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents Preface ix Preface to the Second Edition xiii Notation and Terminology Notation 0.1. Terminology 0.2. xv xv xvi Part 1. 1 Exercises Chapter 1. General Notions: Sets, Functions et al. Essential Background 1.1. 1.1.1. Sets 1.1.2. Functions 1.1.3. Equivalence Relation 1.1.4. Consequences of The Least Upper Bound Property 1.1.5. Countability 1.2. Exercises With Solutions More Exercises 1.3. 3 3 3 9 15 15 17 19 24 Chapter 2.1. 2.1.1. 2.1.2. 2.1.3. 2.1.4. 2.2. 2.3. 2.4. 2.5. 2. Metric Spaces Essential Background Definitions and Examples Important Sets in Metric Spaces Continuity in Metric Spaces Equivalent Metrics True or False: Questions Exercises With Solutions Tests More Exercises 27 27 27 ЗО 32 34 36 36 42 43 Chapter 3.1. 3.1.1. 3.1.2. 3.1.3. 3. Topological Spaces Essential Background General Notions Separation Axioms Closures, Interiors, Limits Points, et al 47 47 47 49 50 V
CONTENTS VI 3.1.4. 3.1.5. 3.1.6. 3.2. 3.3. 3.4. 3.5. Bases and Subbases The Subspace Topology The Product and Quotient Topologies True or False: Questions Exercises With Solutions Tests More Exercises 56 58 59 61 63 72 73 Chapter 4.1. 4.1.1. 4.1.2. 4.1.3. 4.1.4. 4.2. 4.3. 4.4. 4.5. 4. Continuity and Convergence Essential Background Continuity Convergence Sequential Continuity A Word on Infinite Product Topology True or False: Questions Exercises With Solutions Tests More Exercises 77 77 77 82 83 84 86 87 94 95 Chapter 5.1. 5.1.1. 5.1.2. 5.1.3. 5.2. 5.3. 5.4. 5.5. 5. Compact Spaces Essential Background Compactness: General Notions Compactness and Continuity Sequential Compactness and Total Boundedness True or False: Questions Exercises With Solutions Tests More Exercises 99 99 99 102 104 106 107 112 113 Chapter 6.1. 6.1.1. 6.1.2. 6.1.3. 6.2. 6.3. 6.4. 6.5. 6. Connected Spaces Essential Background Connectedness Components Path-connectedness True or False: Questions Exercises With Solutions Tests More Exercises 117 117 117 119 120 122 123 125 126 Chapter 7.1. 7.1.1. 7.1.2. 7. Complete Metric Spaces Essential Background Completeness Fixed Point Theorem 129 129 129 135
7.1.3. 7.2. 7.3. 7.4. 7.5. Chapter 8.1. 8.1.1. 8.1.2. 8.1.3. 8.2. 8.3. 8.4. 8.5. Part 2. CONTENTS vii A Word on Integral Equations True or False: Questions Exercises With Solutions Tests More Exercises 137 140 141 148 148 8. Function Spaces Essential Background Types of Convergence Weierstrass Approximation Theorem The Arzelà-Ascoli Theorem True or False: Questions Exercises With Solutions Tests More Exercises Solutions 153 153 153 155 155 157 157 159 159 161 Chapter 1. General Notions: Sets, Functions et al Solutions to Exercises 1.2. 163 163 Chapter 2.2. 2.3. 2.4. 2. Metric Spaces True or False: Answers Solutions to Exercises Hints/Answers to Tests 181 181 183 201 Chapter 3.2. 3.3. 3.4. 3. Topological Spaces True or False: Answers Solutions to Exercises Hints/Answers to Tests 203 203 209 241 Chapter 4.2. 4.3. 4.4. 4. Continuity and Convergence True or False: Answers Solutions to Exercises Hints/Answers to Tests 243 243 247 266 Chapter 5.2. 5.3. 5.4. 5. Compact Spaces True or False: Answers Solutions to Exercises Hints/Answers to Tests 269 269 272 293 Chapter 6.2. 6.3. 6.4. 6. Connected Spaces True or False: Answers Solutions to Exercises Hints/Answers to Tests 295 295 298 307
CONTENTS viii Chapter 7.2. 7.3. 7.4. 7. Complete Metric Spaces True or False: Answers Solutions to Exercises Hints/Answers to Tests 309 309 313 342 Chapter 8.2. 8.3. 8.4. 8. Function Spaces True or False: Answers Solutions to Exercises Hints/Answers to Tests 343 343 345 350 Bibliography 351 Index 353
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
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| isbn | 9789813146938 9789813148024 |
| language | English |
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| physical | xvii, 356 Seiten |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | World Scientific |
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| spelling | Mortad, Mohammed Hichem 1978- Verfasser (DE-588)1123528640 aut Introductory topology exercises and solutions Mohammed Hichem Mortad (University of Oran 1, Ahmed Ben Bella, Algeria) Second edition New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai World Scientific [2017] xvii, 356 Seiten txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Topology Problems, exercises, etc Topologie (DE-588)4060425-1 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Topologie (DE-588)4060425-1 s Topologischer Raum (DE-588)4137586-5 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029261305&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mortad, Mohammed Hichem 1978- Introductory topology exercises and solutions Topology Problems, exercises, etc Topologie (DE-588)4060425-1 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4137586-5 |
| title | Introductory topology exercises and solutions |
| title_auth | Introductory topology exercises and solutions |
| title_exact_search | Introductory topology exercises and solutions |
| title_full | Introductory topology exercises and solutions Mohammed Hichem Mortad (University of Oran 1, Ahmed Ben Bella, Algeria) |
| title_fullStr | Introductory topology exercises and solutions Mohammed Hichem Mortad (University of Oran 1, Ahmed Ben Bella, Algeria) |
| title_full_unstemmed | Introductory topology exercises and solutions Mohammed Hichem Mortad (University of Oran 1, Ahmed Ben Bella, Algeria) |
| title_short | Introductory topology |
| title_sort | introductory topology exercises and solutions |
| title_sub | exercises and solutions |
| topic | Topology Problems, exercises, etc Topologie (DE-588)4060425-1 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| topic_facet | Topology Problems, exercises, etc Topologie Topologischer Raum |
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