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.
• General topology is one of the most basic disciplines in mathematics, which makes the potential audience fairly large
• With all the following advantages, this book is particularly suitable for beginners: research frontier in topology are contained; few prerequisites are required; brief and self-contained style; emphasis on the most basic concepts and ideas; key concepts appear repeatedly; indices are collected comprehensively for the sake of research
• Beyond the above attributes, this book is in one of the first batch of books in general topology written in English by an author in China. In view of the quick development of mathematical book publishing currently happening in China, this book has a considerable potential for attracting Chinese authors to reference it