Metric Space Topology: Examples, Exercises And Solutions (Paperback)

This introductory book contains a rich collection of exercises and worked examples in Metric Spaces. Other than questions in the traditional setting, plenty of True-or-False type questions and open-ended questions are included. With detailed solutions, these are highly effective in helping students gain a bird's eye view and master the subject and pitfalls better. The presentation is clear in nurturing the mathematical insights and mathematical maturity of the readers. In this book, the pictorialization or visualization of abstract situations into simple pictures is very often crucially conducive to the understanding of the materials. This serves to give an insightful view of the intricate problems, as well as a clue or a direction to formulate rigorous arguments. The learning outcomes include: Demonstrate knowledge and understanding of the basic features of mathematical analysis and point set topology (e.g., able to identify objects that are topologically equivalent); Apply knowledge and skills acquired in mathematical analysis to analyze and handle novel situations in a critical way (e.g., able to determine whether a specific function is uniformly continuous); Think creatively and laterally to generate innovative examples and solutions to non-standard problems (e.g., able to construct counterexamples to inaccurate mathematical statements). Acquire sufficient background for further studies in Functional Analysis, Real Analysis, Differential Geometry, Complex Analysis, Algebraic Geometry, Probability Theory, Mathematical Physics, Economics, and others.

Wing-Sum Cheung is a full Professor of the Department of Mathematics of the University of Hong Kong. He holds a BSc (with 1st class honors) from the Chinese University of Hong Kong, a MA and a PhD from Harvard University. He has served as Head of Department of Mathematics and Associate Dean of the Faculty of Science of the University of Hong Kong, Vice-President of the Hong Kong Mathematical Society, Council Member of the Southeast Asian Mathematical Society, Council Member of the Hong Kong Institute of Science, Leader of the Hong Kong International Olympiad Team, and Honorary Consultant of the Ministry of Education, Youth and Sports of the Government of Cambodia. He has published over 200 journal articles, conference proceedings and book chapters, in which over 140 appeared in ISI journals. He has been named as one of the top 1% highly cited researchers in the world by Clarivate Analytics' Essential Science Indicator for 6 times in the last decade. He is on the editorial board of a number of international mathematical journals including Abstract and Applied Analysis, Asian European Journal of Mathematics, Far East Journal of Mathematical Sciences, Journal of Inequalities and Applications, etc. His current research interests include Differential Geometry, Exterior Differential Systems, Calculus of Variations, Analytic Inequalities, and Differential Equations.