A Comprehensive Textbook on Metric Spaces

Surinder Pal Singh Kainth

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Hardback

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English

Springer Verlag, Singapore
31 October 2023

Calculus & mathematical analysis; Topology

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.

By: Surinder Pal Singh Kainth
Imprint: Springer Verlag, Singapore
Country of Publication: Singapore
Edition: 2023 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 705g
ISBN: 9789819927371
ISBN 10: 9819927374
Pages: 344
Publication Date: 31 October 2023
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

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.

Reviews for A Comprehensive Textbook on Metric Spaces

“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)