Lecture Notes On General Topology - Hardcover

Über die Autorin bzw. den Autor

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 2018–2019 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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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.