Basic Topology 1: Metric Spaces and General Topology

This first of the three-volume book is a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology, including compactness and connectedness, and includes the Stone–Cech compactification and Alexandroff one-point compactification. It also covers the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand–Kolmogoroff theorem.

Format: Hardback
Length: 502 pages
Publication date: 04 July 2022
Publisher: Springer Verlag, Singapore

This comprehensive three-volume textbook serves as a foundational course in topology for undergraduate and graduate students of mathematics. It delves into the study of metric spaces and general topology, providing a solid foundation for understanding these complex concepts. The book begins by introducing the metric, an abstraction of distance in Euclidean space, as the central concept of topology. The unique structure of a metric space gives rise to a topology that finds numerous applications in modern analysis and modern algebra, as demonstrated throughout this volume.

In addition to exploring topological properties such as compactness and connectedness, this study also covers important topics such as the Stone-Cech compactification and the Alexandroff one-point compactification. The volume includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand-Kolmogoroff theorem, which are fundamental tools in topology.

The content of this volume is organized into eight chapters, with the final chapter serving as a historical overview of metric spaces and the development of topology. It provides insights into the motivations behind the emergence of these concepts and their significance in the field. While the book is designed to be a comprehensive introduction to topology for beginners, it also offers valuable insights and advanced topics for students pursuing advanced courses.

One of the key strengths of this textbook is its balanced and unified approach to the subject. It covers a wide range of theories and applications in a clear and concise manner, ensuring that students gain a comprehensive understanding of the topic. The book encourages active learning and promotes a deeper understanding of topology through its engaging writing style and numerous examples and exercises.

Overall, this three-volume textbook is an essential resource for students interested in topology, mathematics, and related fields. It provides a solid foundation for understanding metric spaces and general topology, and its comprehensive coverage of theories and applications makes it suitable for both beginner and advanced students. Whether you are a student seeking to expand your knowledge in topology or a professional looking to advance your expertise, this book is an invaluable tool for your studies.

Weight: 972g
Dimension: 164 x 241 x 37 (mm)
ISBN-13: 9789811665080
Edition number: 1st ed. 2022