Point-Set Topology: A Working Textbook

This  textbook offers a hands-on introduction to general topology, a  fundamental tool in mathematics and its applications. It provides solid  foundations for further study in mathematics in general, and topology in  particular.

Aimed at undergraduate students in  mathematics with no previous exposure to topology, the book presents key  concepts in a mathematically rigorous yet accessible manner,  illustrated by numerous examples. The essential feature of the book is  the large sets of worked exercises at the end of each chapter. All of  the basic topics are covered, namely, metric spaces, continuous maps,  homeomorphisms, connectedness, and compactness. The book also explains  the main constructions of new topological spaces such as product spaces  and quotient spaces. The final chapter makes a foray into algebraic  topology with the introduction of the fundamental group.

Thanks to nearly 300 solved exercises and abundant examples, Point-Set Topology is especially suitable for supplementing a first lecture course on  topology for undergraduates, and it can also be utilized for independent  study. The only prerequisites for reading the book are familiarity with  mathematical proofs, some elements of set theory, and a good grasp of  calculus.