E-Book, Englisch, 222 Seiten, Web PDF
Pervin / Boas Foundations of General Topology
1. Auflage 2014
ISBN: 978-1-4832-2515-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 222 Seiten, Web PDF
ISBN: 978-1-4832-2515-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Foundations of General Topology presents the value of careful presentations of proofs and shows the power of abstraction. This book provides a careful treatment of general topology. Organized into 11 chapters, this book begins with an overview of the important notions about cardinal and ordinal numbers. This text then presents the fundamentals of general topology in logical order processing from the most general case of a topological space to the restrictive case of a complete metric space. Other chapters consider a general method for completing a metric space that is applicable to the rationals and present the sufficient conditions for metrizability. This book discusses as well the study of spaces of real-valued continuous functions. The final chapter deals with uniform continuity of functions, which involves finding a distance that satisfies certain requirements for all points of the space simultaneously. This book is a valuable resource for students and research workers.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Foundations of General Topology;4
3;Copyright Page;5
4;Table of Contents;10
5;Dedication;6
6;Preface;8
7;Chapter 1. Algebra of Sets;14
7.1;1.1 Sets and Subsets;14
7.2;1.2 Operations on Sets;17
7.3;1.3 Relations;19
7.4;1.4 Mappings;23
7.5;1.5 Partial Orders;27
8;Chapter 2. Cardinal and Ordinal Numbers;30
8.1;2.1 Equipotent Sets;30
8.2;2.2 Cardinal Numbers;34
8.3;2.3 Order Types;39
8.4;2.4 Ordinal Numbers;42
8.5;2.5 Axiom of Choice;46
9;Chapter 3. Topological Spaces;49
9.1;Introduction;49
9.2;3.1 Open Sets and Limit Points;49
9.3;3.2 Closed Sets and Closure;52
9.4;3.3 Operators and Neighborhoods;56
9.5;3.4 Bases and Relative Topologies;59
10;Chapter 4. Connectedness, Compactness, and Continuity;64
10.1;4.1 Connected Sets and Components;64
10.2;4.2 Compact and Countably Compact Spaces;69
10.3;4.3 Continuous Functions;73
10.4;4.4 Homeomorphisms;77
10.5;4.5 Arcwise Connectivity;80
11;Chapter 5. Separation and Countability Axioms;82
11.1;5.1 T0- and T1-Spaces;82
11.2;5.2 T2-Spaces and Sequences;86
11.3;5.3 Axioms of Countability;92
11.4;5.4 Separability and Summary;97
11.5;5.5 Regular and Normal Spaces;100
11.6;5.6 Completely Regular Spaces;108
12;Chapter 6. Metric Spaces;112
12.1;6.1 Metric Spaces as Topological Spaces;112
12.2;6.2 Topological Properties;117
12.3;6.3 Hilbert (I2) Space;121
12.4;6.4 Fréchet Space;125
12.5;6.5 Space of Continuous Functions;128
13;Chapter 7. Complete Metric Spaces;131
13.1;7.1 Cauchy Sequences;131
13.2;7.2 Completions;135
13.3;7.3 Equivalent Conditions;138
13.4;7.4 Baire Theorem;140
14;Chapter 8. Product Spaces;142
14.1;8.1 Finite Products;142
14.2;8.2 Product Invariant Properties;145
14.3;8.3 Metric Products;148
14.4;8.4 Tichonov Topology;151
14.5;8.5 Tichonov Theorem;155
15;Chapter 9. Function and Quotient Spaces;160
15.1;9.1 Topology of Pointwise Convergence;160
15.2;9.2 Topology of Compact Convergence;162
15.3;9.3 Quotient Topology;166
16;Chapter 10. Metrization and Paracompactness;171
16.1;10.1 Urysohn's Metrization Theorem;171
16.2;10.2 Paracompact Spaces;173
16.3;10.3 Nagata-Smirnov Metrization Theorem;182
17;Chapter 11. Uniform Spaces;187
17.1;11.1 Quasi Uniformization;187
17.2;11.2 Uniformization;191
17.3;11.3 Uniform Continuity;197
17.4;11.4 Completeness and Compactness;201
17.5;11.5 Proximity Spaces;206
18;Bibliography;210
19;Index;214
