An Introduction to Metric Spaces

This book is a textbook for an introductory course in metric spaces, presenting the basics in a natural and intuitive way while encouraging geometric thinking and active participation in learning. It is divided into seven chapters with diagrammatic illustrations, systematic strategies for proofs, remarks, observations, and exercises.

Format: Paperback / softback
Length: 286 pages
Publication date: 01 February 2022
Publisher: Taylor & Francis Ltd

This comprehensive textbook serves as an essential resource for undergraduate and graduate students embarking on a journey into the world of metric spaces. With a clear objective to present the fundamentals of metric spaces in a natural and intuitive manner, the authors have crafted a text that encourages active participation and a geometric mindset among students.

The book is organized into seven chapters, each dedicated to exploring key concepts and theorems in metric spaces. Introductory concepts, completeness, compactness, connectedness, continuous functions, and metric fixed point theorems with applications are covered in depth, providing a solid foundation for further study.

One of the notable strengths of this textbook is its use of diagrammatic illustrations. These visual representations not only enhance understanding but also encourage readers to think geometrically, aiding in the comprehension of complex concepts. The systematic approach to generating ideas for the proofs of theorems is another key feature, empowering students to develop a deeper understanding of the subject matter.

Throughout the text, there are abundant remarks, observations, and a wide range of exercises designed to reinforce learning and promote critical thinking. Historical notes and brief biographies of influential figures in the development of metric spaces add depth and context to the material, providing valuable insights into the historical significance of metric spaces and their applications.

Whether you are a novice in the field or seeking to deepen your knowledge, this textbook is an invaluable resource. Its clear explanations, engaging illustrations, and comprehensive coverage make it an essential tool for anyone interested in metric spaces and their applications. By fostering a geometric mindset and providing a solid foundation in metric spaces, this textbook equips students with the skills and knowledge necessary to excel in their academic pursuits and pursue careers in mathematics and related fields.

Dimension: 234 x 156 (mm)
ISBN-13: 9780367493493