Overview
- Presents a comprehensive course on metric spaces containing chapters on homeomorphisms, cardinality and the Cantor set
- Delves into axiomatic set theory and proofs through games
- Contains 966 exercises, 144 references, historical insights, a few open questions and some recent results
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About this book
This textbook provides a comprehensive course in metric spaces. Presenting a smooth takeoff from basic real analysis to metric spaces, every chapter of the book presents a single concept, which is further unfolded and elaborated through related sections and subsections. Apart from a unique new presentation and being a comprehensive textbook on metric spaces, it contains some special concepts and new proofs of old results, which are not available in any other book on metric spaces. It has individual chapters on homeomorphisms and the Cantor set. This book is almost self-contained and has an abundance of examples, exercises, references and remarks about the history of basic notions and results. Every chapter of this book includes brief hints and solutions to selected exercises. It is targeted to serve as a textbook for advanced undergraduate and beginning graduate students of mathematics.
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Reviews
“This textbook provides a student-friendly transition from real analysis to general metric spaces. The book is rich in examples and exercises … . This book surveys many interesting results in the theory of metric spaces. Moreover, it contains more than 900 exercises across chapters and appendices. Many of these exercises are original … . The book is a very welcome addition to the literature on metric space theory and it is very valuable for graduate mathematical students.” (Oleksiy Dovgoshey, zbMATH 1547.54001, 2024)
Authors and Affiliations
About the author
Surinder Pal Singh Kainth is Assistant Professor at the Department of Mathematics, Panjab University, Chandigarh, India. He has a Ph.D. degree in integration theory from the Indian Institute of Technology Bombay and is working in generalized integrals and graph theory. He has made some significant progress on the sphere-of-influence graph (SIG) dimension conjecture.
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Bibliographic Information
Book Title: A Comprehensive Textbook on Metric Spaces
Authors: Surinder Pal Singh Kainth
DOI: https://doi.org/10.1007/978-981-99-2738-8
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023
Hardcover ISBN: 978-981-99-2737-1Published: 31 October 2023
Softcover ISBN: 978-981-99-2740-1Published: 01 November 2024
eBook ISBN: 978-981-99-2738-8Published: 30 October 2023
Edition Number: 1
Number of Pages: XVI, 344
Number of Illustrations: 10 b/w illustrations, 2 illustrations in colour