Introduction to Metric Spaces

This book serves as a textbook for an introductory course in metric spaces for undergraduate or graduate students. The goal is to present the basics of metric spaces in a natural and intuitive way and encourage students to think geometrically while actively participating in the learning of this subject. In this book, the authors illustrated the strategy of the proofs of various theorems that motivate readers to complete them on their own. Bits of pertinent history are infused in the text, including brief biographies of some of the central players in the development of metric spaces. The textbook is divided into seven chapters that contain the main materials on metric spaces; namely, introductory concepts, completeness, compactness, connectedness, continuous functions and metric fixed point theorems with applications.Some of the noteworthy features of this book include· Diagrammatic illustrations that encourage readers to think geometrically· Focus on systematic strategy to generate ideas for the proofs of theorems· A wealth of remarks, observations along with a variety of exercises· Historical notes and brief biographies appearing throughout the text

Dr. Dhananjay Gopal has a doctorate in Mathematics from Guru GhasidasUniversity, Bilaspur, India, and is currently Assistant Professor of AppliedMathematics in S V National Institute of Technology, Surat, Gujarat, India.He is author and co-author of several papers in journals, proceedings, and amonograph on Background and Recent Developments of Metric Fixed PointTheory. He is devoted to general research on the theory of Nonlinear Analysisand Fuzzy Metric Fixed Point Theory.Mr. Aniruddha Deshmukh is currently a student of (Integrated) MScMathematics and is associated to the Applied Mathematics and HumanitiesDepartment, S V National Institute of Technology, Surat, Gujarat, India. Hehas been an active student in the department and has initiated many activitiesfor the benefit of the students, especially as a member of the science community(student chapter), known by the name of SCOSH. During his course,he has also attended various internships and workshop such as the MathematicsTraining and Talent Search (MTTS) Programme for two consecutiveyears (2017–2018) and has also done a project on the qualitative questions onDifferential Equations at Indian Institute of Technology (IIT), Gandhinagar,Gujarat, India in 2019. He has also qualified CSIR-NET JRF. Furthermore,his research interest focuses on Linear Algebra and Analysis and their applicabilityin solving some real-world problems.Abhay S. Ranadive is a Professor at the Department of Pure & AppliedMathematics Ghasidas Vishwavidyalaya (A Central University), Bilaspur,Chattisgarh, India. He has been teaching at the university for the last 30years. He is author and co-author of several papers in journals and proceedings.He is devoted to general research on the theory of fuzzy sets and fuzzylogic, modules, and metric fixed point.Mr. Shubham Yadav is currently a student of (Integrated) M.Sc. Mathematicsand is associated to the Applied Mathematics and Humanities Department,S V National Institute of Technology, Surat, Gujarat, India. As amember of SCOSH the student prominent science community in the institute,he has attended and organized various workshops and seminars. He alsoattended Madhava Mathematics Camp 2017. He did an internship on the calculusof fuzzy numbers at NIT, Trichy and one on operator theory at IIT,Hyderabad. He has also qualified for JRF. His main research interests arefunctional analysis and fuzzy sets with a knack for learning abstract mathematicalconcepts.