This book offers the comprehensive study of one of the foundational topics in Mathematics, known as Metric Spaces. The book delivers the concepts in an appropriate and concise manner, at the same time rich in illustrations and exercise problems. Special focus has been laid on important theorems like Baire’s Category theorem, Heine–Borel theorem, Ascoli–Arzela Theorem, etc, which play a crucial role in the study of metric spaces.The additional chapter on Cofinal completeness, UC spaces and finite chainability makes the text unique of its kind. This helps the students in: taking the secondary step towards analysis on metric spaces, realizing the connection between the two most important classes of functions, continuous functions and uniformly continuous functions, understanding the gap between compact metric spaces and complete metric spaces.Readers will also find brief discussions on various subtleties of continuity like subcontinuity, upper semi-continuity, lower semi-continuity, etc. The interested readers will be motivated to explore the special classes of functions between metric spaces to further extent.Consequently, the book becomes a complete package: it makes the foundational pillars strong and develops the interest of students to pursue research in metric spaces. The book is useful for third and fourth year undergraduate students and it is also helpful for graduate students and researchers.Key FeaturesThe concise presentation of the fundamental topics will help in building the understanding of the conceptsWell organization of significant theorems makes the book more reader friendlyAdditional chapter on Cofinal completeness, UC spaces and finitely chainable spaces will help the interested students to step in a vibrant area of researchIt covers wide range of concepts which makes the text self-sufficient for undergraduate students as well as teachers who are teaching metric spacesIt includes various interesting exercises which could be taken as topics for projects at undergraduate and graduate level

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