Metric Spaces

Subhajit Paul (Autor)

Buch | Hardcover

320 Seiten

2026
Springer Nature Switzerland AG (Verlag)
978-981-96-9258-3 (ISBN)

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This book systematically develops the theory of Metric Spaces while serving as a connection between classical Real Analysis and General Topology. It is designed for senior undergraduate and graduate students, providing formal definitions, theorems, proofs, examples, remarks, exercises, and explanatory notes. Instructors can use the numerous examples and miscellaneous results to structure their teaching approach. The book contains seven chapters, first of which lists primary results (without proofs) from the undergraduate Real Analysis course. Each subsequent chapter builds on cues from previous levels, adapting them to the context of Metric Spaces.Additionally, the book includes four appendix chapters. The first three are included to maintain the flow of discussion in the main chapters, relegating less relevant proofs to the appendices. The fourth appendix on the Cantor set is included to provide insight into this notable mathematical concept.

Subhajit Paul has been an Assistant Professor in the Department of Mathematics at Salesian College (Autonomous), Siliguri, West Bengal, India, since 2013. He served as the Head of the department from 2016 to 2024. Currently, he holds the position of Dean of Faculty of Sciences at the same college. He received his Master’s degree from the Tata Institute of Fundamental Research, Centre for Applicable Mathematics (TIFR-CAM), Bengaluru, Karnataka, India, in 2010.

Chapter 1. Recollections.- Chapter 2. Basic Notions.- Chapter 3. Topology of Metric Spaces 4. Completeness.- Chapter 5. Continuity.- Chapter 6. Compactness.- Chapter 7. Connectedness.

Erscheinungsdatum	13.06.2025
Reihe/Serie	University Texts in the Mathematical Sciences
Zusatzinfo	83 Illustrations, black and white
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Compactness • Completeness • connectedness • Continuity • Metric Spaces • set theory • Topology
ISBN-10	981-96-9258-X / 981969258X
ISBN-13	978-981-96-9258-3 / 9789819692583
Zustand	Neuware