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E-raamat: Lecture Notes On General Topology

(Beijing Inst Of Technology, China)
  • Formaat: 150 pages
  • Ilmumisaeg: 17-Dec-2020
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789811227431
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Lecture Notes On General TopologySuurem pilt
  • Formaat: 150 pages
  • Ilmumisaeg: 17-Dec-2020
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789811227431
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This book is intended as a one-semester course in general topology, a.k.a. point-set topology, for undergraduate students as well as first-year graduate students.

This book is intended as a one-semester course in general topology, a.k.a. point-set topology, for undergraduate students as well as first-year graduate students. Such a course is considered a prerequisite for further studying analysis, geometry, manifolds, and certainly, for a career of mathematical research. Researchers may find it helpful especially from the comprehensive indices.General topology resembles a language in modern mathematics. Because of this, the book is with a concentration on basic concepts in general topology, and the presentation is of a brief style, both concise and precise. Though it is hard to determine exactly which concepts therein are basic and which are not, the author makes efforts in the selection according to personal experience on the occurrence frequency of notions in advanced mathematics, and to related books that have received admirable reviews.This book also contains exercises for each chapter with selected solutions. Interrelationships among concepts are taken into account frequently. Twelve particular topological spaces are repeatedly exploited, which serve as examples to learn new concepts based on old ones.
Chapter 1 Introduction
1(8)
Exercises 1
6(1)
Selected Solutions 1
7(2)
Chapter 2 Topological Spaces
9(30)
2.1 Topological structures
9(4)
2.2 Subspace topology
13(2)
2.3 Covers
15(3)
2.4 Point position with respect to a set
18(4)
2.5 Metrics and the metric topology
22(8)
Exercises 2
30(4)
Selected Solutions 2
34(5)
Chapter 3 Continuous Maps and Homeomorphisms
39(20)
3.1 Continuous maps
40(8)
3.2 Homeomorphisms
48(5)
3.3 Topological properties
53(2)
Exercises 3
55(3)
Selected Solutions 3
58(1)
Chapter 4 Connectedness
59(18)
4.1 Connected spaces
59(8)
4.2 Path-Connectedness
67(4)
Exercises 4
71(3)
Selected Solutions 4
74(3)
Chapter 5 Separation and Countability Axioms
77(16)
5.1 Axioms T0, Ti, T2, T3, and T4
77(4)
5.2 Hausdorff spaces
81(1)
5.3 Regular spaces and normal spaces
82(6)
5.4 Countability axioms
88(3)
Exercises 5
91(1)
Selected Solutions 5
92(1)
Chapter 6 Compactness
93(14)
6.1 Compact spaces
93(4)
6.2 Interaction of compactness with other topological properties
97(5)
6.3 Gromov-Hausdorff distance
102(3)
Exercises 6
105(1)
Selected Solutions 6
106(1)
Chapter 7 Product Spaces and Quotient Spaces
107(20)
7.1 Product spaces
107(8)
7.2 Quotient spaces
115(8)
Exercises 7
123(2)
Selected Solutions 7
125(2)
Appendix A Some Elementary Inequalities 127(4)
Bibliography 131(4)
Author Index 135(2)
Subject Index 137
Guoliang Wang is a full professor in the School of Mathematics and Statistics at Beijing Institute of Technology (BIT). He received his B.A. from the School of Mathematical Sciences at Peking University in 2005, and PhD from the Center for Combinatorics (CFC) at Nankai University under the supervision of William Y C Chen in 2010. After that he was a postdoc at Beijing International Center for Mathematical Research (BICMR) and the University of Haifa for two years respectively. Then he was a visiting associate professor at MIT in the 20182019 academic year. Professor Wang is the author of more than 30 research papers in algebraic combinatorics. One of his works in topological graph theory was awarded the unique First Prize for Excellent Papers of Youths by the combinatorics sub-society in the Operations Research Society of China.
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