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001482745 001__ 1482745
001482745 003__ OCoLC
001482745 005__ 20231128003349.0
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001482745 019__ $$a1409029651
001482745 020__ $$a9789819927388$$q(electronic bk.)
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001482745 020__ $$z9819927374
001482745 020__ $$z9789819927371
001482745 0247_ $$a10.1007/978-981-99-2738-8$$2doi
001482745 035__ $$aSP(OCoLC)1407025704
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001482745 050_4 $$aQA611.28
001482745 08204 $$a514/.325$$223/eng/20231115
001482745 1001_ $$aKainth, Surinder Pal Singh.
001482745 24512 $$aA comprehensive textbook on metric spaces /$$cSurinder Pal Singh Kainth.
001482745 260__ $$aSingapore :$$bSpringer,$$c2023.
001482745 300__ $$a1 online resource
001482745 504__ $$aIncludes bibliographical references and index.
001482745 5050_ $$aIntro -- Foreword -- Preface -- Contents -- 1 Real Analysis -- 1.1 The Real Number System -- 1.2 Sequences of Real Numbers -- 1.2.1 Convergence of a Sequence -- 1.2.2 Algebra of Limits -- 1.2.3 Bounded Monotone Sequences -- 1.2.4 Cauchy Sequences -- 1.3 Series Convergence -- 1.4 Decimal and General Expansions -- 1.5 Continuity -- 1.6 Uniform Convergence -- 1.6.1 Necessary and Sufficient Conditions -- 1.6.2 Notes and Remarks -- 1.7 Hints and Solutions to Selected Exercises -- References -- 2 Metric Spaces -- 2.1 Introduction -- 2.1.1 The Euclidean Spaces -- 2.1.2 Balls and Bounded Sets
001482745 5058_ $$a2.2 Convergence in Metric Spaces -- 2.3 Normed Linear Spaces -- 2.4 Sequence Spaces -- 2.5 Hints and Solutions to Selected Exercises -- References -- 3 Topology -- 3.1 Open Sets and Closed Sets -- 3.2 Limit Points and Isolated Points -- 3.3 Closures and Boundaries -- 3.4 Subspace Topology -- 3.5 Limits and Continuity -- 3.5.1 The Case of Euclidean Spaces -- 3.5.2 Continuity and Uniform Convergence -- 3.6 Topology of Normed Linear Spaces -- 3.7 Hints and Solutions to Selected Exercises -- References -- 4 Completeness -- 4.1 Introduction -- 4.2 Banach Contraction Principle
001482745 5058_ $$a4.3 Characterizations of Completeness -- 4.3.1 Cantor Intersection Property -- 4.3.2 Totally Bounded Sets -- 4.4 Completion of a Metric Space -- 4.5 Banach Spaces -- 4.6 Hints and Solutions to Selected Exercises -- References -- 5 Compactness -- 5.1 Introduction -- 5.1.1 Compact Sets and Closed Sets -- 5.1.2 Compact Subsets of Euclidean Spaces -- 5.2 Characterizations of Compact Sets -- 5.2.1 Finite Intersection Property -- 5.2.2 Sequentially Compact Sets -- 5.3 Continuity and Compactness -- 5.3.1 Uniform Continuity -- 5.3.2 Notes and Remarks -- 5.4 Lipschitz Continuity
001482745 5058_ $$a5.5 Hints and Solutions to Selected Exercises -- References -- 6 Connectedness -- 6.1 Path Connectedness -- 6.2 Connected Sets -- 6.3 Components -- 6.4 Miscellaneous -- 6.4.1 Locally Connected and Locally Path Connected Spaces -- 6.4.2 Path Connectedness in Locally Path Connected Spaces -- 6.4.3 Quasi-components -- 6.4.4 Totally Disconnected Sets -- 6.5 Hints and Solutions to Selected Exercises -- References -- 7 Cardinality -- 7.1 Countable and Uncountable Sets -- 7.2 Some Applications to Topology -- 7.3 The Set of Discontinuities -- 7.3.1 The Case of Monotone Functions -- 7.3.2 The General Case
001482745 5058_ $$a7.4 Cardinality -- 7.4.1 Cardinal Numbers -- 7.4.2 Notes and Remarks -- 7.5 Hints and Solutions to Selected Exercises -- References -- 8 Denseness -- 8.1 Separability -- 8.2 Perfect Sets -- 8.3 Baire Category Theorem -- 8.4 Equicontinuity -- 8.5 Hints and Solutions to Selected Exercises -- References -- 9 Homeomorphisms -- 9.1 Equivalent Metrics -- 9.2 Homeomorphisms -- 9.3 Extension Theorems for Continuous Functions -- 9.4 Finite-Dimensional Normed Linear Spaces -- 9.5 Hints and Solutions to Selected Exercises -- References -- 10 The Cantor Set -- 10.1 Introduction
001482745 506__ $$aAccess limited to authorized users.
001482745 520__ $$aThis textbook provides a comprehensive course in metric spaces. Presenting a smooth takeoff from basic real analysis to metric spaces, every chapter of the book presents a single concept, which is further unfolded and elaborated through related sections and subsections. Apart from a unique new presentation and being a comprehensive textbook on metric spaces, it contains some special concepts and new proofs of old results, which are not available in any other book on metric spaces. It has individual chapters on homeomorphisms and the Cantor set. This book is almost self-contained and has an abundance of examples, exercises, references and remarks about the history of basic notions and results. Every chapter of this book includes brief hints and solutions to selected exercises. It is targeted to serve as a textbook for advanced undergraduate and beginning graduate students of mathematics.
001482745 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed November 15, 2023).
001482745 650_0 $$aMetric spaces.
001482745 655_0 $$aElectronic books.
001482745 77608 $$iPrint version: $$z9819927374$$z9789819927371$$w(OCoLC)1375552778
001482745 852__ $$bebk
001482745 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-99-2738-8$$zOnline Access$$91397441.1
001482745 909CO $$ooai:library.usi.edu:1482745$$pGLOBAL_SET
001482745 980__ $$aBIB
001482745 980__ $$aEBOOK
001482745 982__ $$aEbook
001482745 983__ $$aOnline
001482745 994__ $$a92$$bISE