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This textbook on Metric Spaces is designed for undergraduate students, offering clear and accessible language to facilitate understanding. The examples and exercises are systematically structured to align with academic requirements, aiding students in developing a robust conceptual grasp of the subject. The text strikes a balance between theoretical concepts and practical applications, laying a solid foundation for advanced studies in analysis and topology. Each chapter features carefully selected problems designed to promote logical thinking and reinforce key concepts. This book serves as a valuable resource for both classroom instruction and self-study.
Dr. Neha Bhatia completed her undergraduate education at Deen Dayal Upadhyaya College and her master’s degree at Hindu College, both under the University of Delhi. She is currently serving as an Assistant Professor in the Department of Mathematics at Rajdhani College, University of Delhi. With over nine years of teaching experience, she has taught a wide range of undergraduate courses, including Real Analysis, Differential Equations, and Algebra. She earned her doctorate in 2015 in the field of Operator Theory from the Department of Mathematics, University of Delhi. She has published extensively in reputed national and international journals and is the co-author of the book An Introduction to Abstract Algebra.
Key Features:
Alignment with NEP-2020 Syllabus: The content is structured to align with the
National Education Policy (NEP) 2020 syllabus, ensuring relevance and
comprehensiveness for current academic standards.
Comprehensive Coverage of Fundamental Topics: It thoroughly covers essential
topics such as open and closed sets, continuous mappings, topologies, and
homeomorphisms, providing a solid foundation in metric space theory.
Structured for Progressive Learning: Chapters are organized to progressively build
knowledge, starting from basic definitions to more advanced topics, supporting a
step-by-step learning process.
Extensive Examples and Illustrations: The book includes numerous examples and
illustrations to aid in the understanding of concepts, making it ideal for self-study and
reinforcing classroom learning.
Focus on Logical Reasoning and Problem-Solving: Each chapter includes carefully
selected problems that encourage logical thinking and reinforce key concepts,
enhancing problem-solving skills.
Suitable for Diverse Learning Environments: Designed to be a valuable resource for
both classroom instruction and self-study, accommodating various learning
preferences and environments
1 Introduction
2 Metrics
3 Completeness
4 Continuous Functions
5 Compact Metric Spaces
6 Connectedness
