**Best Reference Books on General Topology**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**General Topology Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on General Topology below.

- General Topology
- Advanced Topology
- Elements of Differential Topology
- Topology and Geometry for Physicists
- Topological Vector Spaces
- Algebraic Topology

## 1. General Topology

1."Introduction to General Topology" by K D Joshi | |

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2."General Topology" by J L Kelly
“General Topology” Book Review: This book offers a thorough and methodical exploration of general topology, with well-organized and concise chapters that lay a solid foundation for modern analysis. The inclusion of self-assessment problems enables readers to practice and test their understanding, while the final section provides an axiomatic approach to set theory. The text also incorporates various counterexamples and real-world applications of general topology, making it a valuable resource for mathematicians working in the field of analysis.
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3."General Topology" by Seymour Lipschutz
“General Topology” Book Review: This updated and revised book explores recent developments and latest topics in general topology. Each reader-friendly chapter efficiently describes and explains each topic with clarity and precision. The book includes many important definitions and theorems of general topology, illustrated with suitable examples. It is also packed with numerous solved problems and practice exercises to provide better practical knowledge and understanding. The book highlights many practical applications of general topology to provide relevant and relatable content to the readers. It will be highly beneficial for mathematics students seeking to gain expertise in the subject.
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4."General Topology" by Stephen Willard
“General Topology” Book Review: This book provides coverage of two major areas of general topology: continuous topology and geometric topology. Its chapters cover all the major topics, including set theory, metric spaces, topological spaces, convergence, separation and countability, compactness, metrizable spaces, connectedness, uniform spaces, and function spaces. In particular, the book highlights the topics of connectivity properties, topological characterization theorems, and homotopy theory. This book is designed for advanced undergraduate students of mathematics who are studying general topology. In the section on continuous topology, the book discusses great detail on topics such as convergence, compactness, metrization, complete metric spaces, uniform spaces, and function spaces. The book introduces many standard spaces for each related problem in every section. It also includes numerous diagrams, examples, historical notes, a bibliography, and an index. Overall, this book is designed for advanced undergraduate and beginning graduate students seeking a thorough understanding of general topology.
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5."General Topology" by John L Kelley
“General Topology” Book Review: This well-structured and organized book covers major aspects and essential concepts of general topology, including topological spaces, Moore-Smith convergence, product and quotient spaces, embedding and metrization, and compact, uniform, and function spaces. It offers thorough explanations, enriched with several examples, problems, and theorems, while also mentioning the applications of general topology in various fields of mathematics. This book provides a strong foundation for modern analysis and will be valuable for graduating students of mathematics and sciences seeking understanding of general topology.
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6."Schaums Outline of General Topology" by Seymour Lipschutz
“Schaum’s Outline of General Topology” Book Review: This book is designed to present specialized topics in topology. Its chapters are precise, and explain each concept step-by-step. The book also introduces the technique of effective problem-solving, with numerous solved and unsolved problems to support the content. The topics featured in this book have been reviewed by experts in their respective fields, making it a valuable source of information. The book mentions the applications of general topology in various fields. This book is suitable for undergraduate and graduate courses in general topology.
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7."Introduction to Topology" by Bert Mendelson and Mathematics
“Introduction to Topology” Book Review: This book offers an excellent introduction to the fundamental principles and concepts of topology. It starts with a clear description of set theory and continues with chapters on metric spaces, topological spaces, connectedness, and compactness. The book is written in an easy-to-understand style, featuring important definitions and theorem proofs. It also includes numerous exercises for self-study and practice. This book will be a valuable resource for both undergraduate and graduate students of mathematics seeking a deeper understanding of calculus.
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8."General Topology" by J Dixmier and S K Berberian
“General Topology” Book Review: This book is focused on presenting fundamental concepts of topology in a clear and concise manner. The theory of real-valued functions of a real variable is illustrated in detail in this text, including topics such as uniform continuity, uniform convergence, equicontinuity, and the Bolzano-Weierstrass theorem. In addition to providing visual support through the inclusion of numerous figures, the book also offers several worked examples and applications to give readers practical knowledge and relatable content. This book will be highly beneficial for both undergraduate and graduate students of mathematics seeking to deepen their understanding of the subject.
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9."General Topology" by N Bourbaki
“General Topology” Book Review: This book offers presentation of all the essential concepts, definitions, and principles of general topology, covering uniform structures, topological spaces, and real numbers and their associated properties. The chapters discusses major topics such as Haar measure, convolution and representations, and measures on Hausdorff topological spaces, with each chapter concluding with a range of exercises for readers to test their understanding. The topics and concepts are clearly explained throughout the text using appropriate examples, and the book also highlights the various applications of general topology in different fields. As such, this book will prove highly valuable for students of mathematics with an interest in topology.
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10."Principles of Topology" by Fred H Croom
“Principles of Topology” Book Review: The book offers a geometric perspective on general topology. The initial section of the book covers metric spaces, general topological spaces, continuity, topological equivalence, basis, subbasis, connectedness, compactness, separation properties, and metrization. The later section focuses on subspaces, product spaces, and quotient spaces, while also introducing geometric, differential, and algebraic topology. The book contains numerous exercises for self-study and self-assessment. It highlights the applications of topological ideas and concepts in geometry and mathematical analysis. This book will be useful resource for undergraduate and graduate students of mathematics studying topology and multivariable calculus.
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11."General Topology" by J L Kelly
“General Topology” Book Review: This book is designed to teach fundamental metric topological methods and algebraic concepts. It starts by introducing the vector character of Euclidean n-space and familiar facts from linear algebra. In addition, the book covers the concepts related to convex body theory and the affine character of space, and explains the analogy between linear and affine concepts. The book explains methods for verifying intuitive relations analytically in spaces of general dimensions, and includes a collection of standard fundamental theorems.
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## 2. Advanced Topology

1."Topology" by S W Davis
“Topology” Book Review: The book is divided into two parts that explore the concept of topology. Part I covers the fundamentals of set theory and topology, while Part II utilizes these concepts to delve into topics such as point-set or set-theoretic topology, algebraic topology, functional analysis, and continuum theory. This book is designed for advanced undergraduate and beginning graduate students who are taking introductory courses in topology.
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2."Topology" by A Pawar P K Chaurasya
“Topology” Book Review: The book provides study of general topology and algebraic topology, with a focus on their real-world applications. It contains a multitude of illustrations, examples, and problems to facilitate a thorough comprehension of the topics covered.
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3."Topology" by J Dugundji
“Topology” Book Review: The initial chapters of this book cover fundamental topics such as elementary set theory, ordinals and cardinals, topological spaces, Cartesian products, and connectedness. The subsequent chapters provide a detailed explanation of identification topology, weak topology, separation axioms, covering axioms, metric spaces, and convergence. The book also discusses topics such as compactness, function spaces, complete spaces, and homotopy. Later chapters cover maps into spheres, topology of En, homotopy type, path spaces, H-spaces, and fiber spaces. The content is presented in a comprehensive manner and is suitable for advanced undergraduate and graduate level students in mathematics.
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4."INTRODUCTION TO TOPOLOGY AND MODERN ANALYSIS" by George Simmons
“Introduction to Topology and Modern Analysis” Book Review: The book provides a thorough coverage of the mathematical concepts of continuity and linearity. It begins by defining these concepts and then explores their interdependence from the perspectives of topology and modern analysis. This book is a valuable resource for students, researchers, and professionals alike.
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5."Topology" by K P Gupta
“Topology” Book Review: This book is a comprehensive textbook covering the fundamentals of topology. The book consists of eight chapters, introducing sets, functions, metric spaces, topological spaces, continuity, connectedness, compactness, and separation axioms. The author provides clear explanations and numerous examples, making the book accessible to undergraduate students and professional mathematicians. The final chapter provides an introduction to algebraic topology. This book is an ideal resource for anyone interested in learning about topology.
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6."Topology: A Geometric Approach" by M Ganesh
“Topology: A Geometric Approach” Book Review: This student-friendly book discusses metric spaces, including normed linear spaces and inner product spaces, in a concise and lucid manner. It is specifically designed for postgraduate level students and provides many worked-out examples and problems to aid in understanding. The concepts are also illustrated with figures for further clarity. The book goes beyond metric spaces to explore affine, projective, and Euclidean geometries of topology, with a particular focus on normed linear spaces, inner product spaces, and both finite and infinite dimensional metric spaces. Each chapter concludes with additional topics in appendices for more in-depth information.
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7."Topology of Metric Spaces" by S Kumaresan
“Topology of Metric Spaces” Book Review: This book provides guide to studying the advanced topics of topology and analysis. Real-world examples are used to illustrate the theorems, which are presented with proofs. The book is specifically aimed at undergraduate students and includes numerical problems and solutions. The foundational concepts are linked to real-world applications, building students’ skills in geometric thinking. The book presents metric space topology using concrete spaces and geometric ideas, while also discussing real analysis and encouraging readers to explore modern analysis. It contains numerous examples of spaces and maps, making it an ideal reference for those studying general topology or point-set topology. This book is suitable for both students and professionals.
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8."Introduction to Topology" by Colin Adams
“Introduction to Topology: Pure and Applied” Book Review: This book provides an introduction to topology, a significant branch of mathematics that finds applications in fields such as science, engineering, economics, and mathematics. The book takes a mathematical approach to explain the fundamentals of topology, starting with the basics of point-set topology and then delving into knots, robotics, and graphs. The book is designed for undergraduate students and includes real-world illustrations to help readers grasp the concepts. The book focuses on the importance of topology in applications to other fields.
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9."Topology" by K Chandrasekhara Rao
“Topology” Book Review: The main focus of this book is to provide coverage of the principles, techniques, and theorems of topology. The initial chapters introduce topics such as Kuratowski closure operator, separation axioms, connectedness, compactness, and paracompactness. The book also explores significant results of the Tychonoff theorem, the Tietze extension theorem, the Urysohn metrization theorem, and the Stone theorem. Later chapters delve into homotopy, metrizability, and bitopological spaces.
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10."Topology and Geometry in Physics" by Bick Steffen
“Topology and Geometry in Physics” Book Review: This book is a guide to the latest advancements and contemporary applications in physical research. It provides an introduction to topological concepts in various fields including supersymmetric solitons, gauge theories, chiral anomalies, BRST quantization, and noncommutative geometry. Presented in the form of extensive lectures, this book is highly recommended for beginners in the field, as well as postgraduate students and lecturers seeking advanced material.
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## 3. Elements of Differential Topology

1."Modern Geometry Methods and applications-II" by A A Dubovin
“Modern Geometry Methods and applications-II” Book Review: This book provides an understanding of the key theories and perspectives on the topic. It delves deeper into the subject matter than a general textbook and is presented in a clear and accessible style for students. The book covers a range of advanced topics such as elasticity, relativity, the theory of tensors, covariant differentiation, Riemannian curvature, geodesics, calculus of variations, conservation laws, and Hamiltonian formalism, as well as skew-symmetric tensors.
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2."Differential Topology" by V Guillemin and A pollack
“Differential Topology” Book Review: This book provides an overview of the topic of functional analysis, along with its various connections to other branches of mathematics. The author presents step-by-step proofs, making the material accessible to readers with only undergraduate analysis and linear algebra background. The book covers a range of topics, including manifolds and smooth maps, transversality and intersection, oriented intersection theory, integration on manifolds, and subtopics such as derivatives and tangents, homotopy and stability, the Borsuk-Ulam theorem, Lefschetz fixed point theory, the Hopf degree theorem, exterior algebra, exterior derivative, and appendices on Measure Zero and Sard’s theorem, and the Classification of Compact One-Manifolds. This book is ideal for introductory graduate courses or advanced undergraduate courses.
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3."Differential Topology" by Morris W Hirsch
“Differential Topology” Book Review: The book presents the subject matter in a methodical and structured way, starting with the basic concepts and properties. The proofs are presented clearly and the book is written in an accessible and approachable style with minimal prerequisites. It covers a range of topics, including Manifolds and Maps, Function Spaces, Transversality, Vector Bundles and Tubular Neighborhoods, Degrees, Intersection Numbers, Euler Characteristic, Morse Theory, Cobordism, Isotopy, Surfaces, and more, along with appendices summarizing background material. The book provides numerous examples to illustrate the theories, ranging from routine to unsolved problems, and highlights further developments in the field. This makes it an ideal reference for advanced undergraduate courses or introductory graduate courses.
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4."Elements of Differential Topology" by Anant R Shastri
“Elements of Differential Topology” Book Review: The topics in this book are presented elegantly. Starting with differential and integral calculus, it guides the reader through the intricacies of manifold theory and covers algebraic topology, algebraic/differential geometry, and Lie groups. The book provides a review of differential and integral calculus, which can be used throughout, and includes exercises with solutions at the end of each chapter. Topics covered include Submanifolds of Euclidean Spaces, Integration on Manifolds, Abstract Manifolds, Isotopy, Intersection Theory, Geometry of Manifolds, Lie Groups and Lie Algebras, etc.
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5."Elements of Topological Dynamics" by J de Vries
“Elements of Topological Dynamics” Book Review: This book provides an introductory overview of the topic, focusing on topological transformation groups and their applications in qualitative theory of differential equations. The material is presented in a systematic and elementary way, making it accessible for readers interested in recent research in this field. The book covers topics such as various aspects of dynamical systems theory, continuous and discrete flows, equicontinuity and distality, structure of extensions, and important examples. The focus is on presenting fundamental methods and techniques, rather than discussing leading problems and their solutions.
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6."Elements of the Theory of Functions and Functional Analysis" by A N Kolmogorov and S V Fomin
“Elements of the Theory of Functions and Functional Analysis” Book Review: This book has been thoroughly updated and streamlined to reflect the latest developments in the field. Its engaging style makes it dynamic and accessible to readers. The book covers a range of topics, including the fundamentals of set theory, metric spaces, normed linear spaces, cardinal numbers, partition into classes, mapping of sets, general concepts of functions, weak convergence, open and closed sets, and complete metric spaces, all with detailed examples. It also discusses important topics such as linear operators, linear operator equations, Fredholm’s Theorems, real functions in metric spaces, Fubini’s Theorem, products of sets and measures, and more.
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7."Differential Topology" by Victor Guillemin and Alan Pollack
“Differential Topology” Book Review: This book provides a contemporary perspective on functional analysis and its connections to other areas of mathematics. The proofs are presented in a step-by-step manner, making the material accessible to undergraduate students with a background in analysis and linear algebra. The book covers topics such as manifolds and smooth maps, transversality and intersection, oriented intersection theory, integration on manifolds, and other subtopics including derivatives and tangents, homotopy and stability, the Borsuk-Ulam theorem, Lefschetz fixed point theory, the Hopf degree theorem, exterior algebra and derivative, and two appendices on measure zero and Sard’s theorem and classification of compact one-manifolds. This book is well-suited for an introductory graduate or advanced undergraduate course.
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8."Differential Topology: First Steps" by Andrew H Wallace
“Differential Topology: First Steps” Book Review: This book presents topology in an intuitive way, avoiding difficult subtleties and technicalities. It starts at an elementary level and progresses to advanced topics, covering all standard material. The focus is mainly on the methods of spherical modifications and the study of critical points of functions on manifolds. The book is self-contained, requiring no prerequisites, and provides introductory material for all topics covered. It includes discussions on Set Theory, Topological Spaces, Open and Closed Sets, Topological Products, Continuous Maps, 3-Manifolds, Non-Orientable Case, Two-Dimensional Manifolds, Modifications, Spherical Modifications, Cobounding Manifolds, Displacement, Isotopy, and interpretation of Theorem 6-5 in Terms of Critical Points.
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9."Differential Topology" by C T C Wall
“Differential Topology” Book Review: The book provides an extensive exploration of the topic by offering a wide perspective on geometric techniques for studying the topology of smooth manifolds. It introduces the concepts of manifold from the first principles and supplements them with appendices on topology and homotopy theory. The book derives deep results from foundational concepts, including a thorough treatment of general position and transversality, proper actions of Lie groups, immersions and embeddings, surgery procedure, and cobordism theory. Its rigorous approach and growing complexity require a basic understanding of the subject matter. Advanced students and researchers can gain accessible entry into the field of differential topology through this well-explained book.
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10."Introduction to Differential Topology" by T Bröcker and K Jänich
“Introduction to Differential Topology” Book Review: This book provides easy-to-understand overview of the fundamental theories and concepts in the topic. The author presents the material in an elementary way, using simple language and detailed explanations of all key topics. The book serves as an introduction to differential manifolds, with a focus on geometric aspects and practical constructions. It features numerous diagrams to illustrate the proofs and includes many problems for the reader to solve. Prior knowledge of analysis and topology is recommended. The book covers a range of topics, including manifolds and differentiable structures, tangent spaces, vector bundles, linear algebra for vector bundles, Sard’s theorem, embedding, dynamical systems, isotopy of embeddings, connected sums, second-order differential equations and sprays, the exponential map and tubular neighborhoods, manifolds with boundary, and transversality.
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## 4. Topology and Geometry for Physicists

1."Topology and Geometry for Physicists (Dover Books on Mathematics)" by Charles Nash and Siddhartha Sen
“Topology and Geometry for Physicists (Dover Books on Mathematics)” Book Review: This book serves as an accessible introduction to geometrical and topological methods in theoretical physics and applied mathematics, with no prerequisite detailed background in topology or geometry. It emphasizes physical motivations, enabling students to apply the techniques to their own physics formulas and research. The book covers a wide range of physics applications, including condensed matter physics, statistical mechanics, and elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection, covariant derivatives, and Morse theory.
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2."Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists" by Paul Renteln
“Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists” Book Review: This book covers the fundamental topics of modern differential geometry and topology in great detail. It covers multilinear algebra, differentiation, and integration on manifolds, Lie groups and Lie algebras, homotopy, and de Rham cohomology. The book also provides a plethora of exercises to test the students’ understanding of the concepts. It demonstrates the essential connections of these concepts with classical mechanics, electromagnetism (including circuit theory), general relativity, and gauge theory through various applications. This book is suitable for undergraduate and graduate students in mathematics and the physical sciences.
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3."Topology for Physicists (Grundlehren der mathematischen Wissenschaften)" by Albert S Schwarz and Silvio Levy
“Topology for Physicists (Grundlehren der mathematischen Wissenschaften)” Book Review: This book discusses the subject of topology and its application in quantum field theory. It explains how nontrivial topological solutions, such as solitons and instantons, allow physicists to move beyond the constraints of perturbation theory. The book also explores topology’s significance in studying defects in condensed media and singularities in crystal excitation spectra. It covers fundamental topology concepts, including homotopy theory, homology theory, and fibration theory, which are essential to quantum field theorists. This book is an excellent resource for physicists and researchers working in the field of topology.
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4."Differential Manifolds: A Basic Approach For Experimental Physicists" by Paul Baillon
“Differential Manifolds: A Basic Approach For Experimental Physicists” Book Review: The focus of this book is to provide an understanding of the basics of differential manifolds, with each element thoroughly proved. The book focuses on the fundamental mathematical concepts essential for the development of differential manifolds, starting from the first principles of set theory and formal logic without requiring any specialized knowledge. The book is significant for research physicists seeking a strong foundation in the field, and it can also aid experimental physicists in manipulating equations and expressions within this framework.
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5."Geometric Algebra for Physicists" by Chris Doran and Anthony Lasenby
“Geometric Algebra for Physicists” Book Review: This book presents the most up-to-date insights into the field of geometric algebra. It begins with a comprehensive introduction to geometric algebra and covers a wide range of topics including innovative methods for handling rotations in any dimension, the relationship between rotations, bivectors, and the structure of Lie groups. It explores the idea of complex analytic function theory in arbitrary dimensions, and its applications in quantum theory and electromagnetism. The book also discusses the applications of geometric algebra in various areas such as black holes and cosmic strings. It is an ideal graduate-level textbook for courses on the physical applications of geometric algebra and is also suitable for researchers in the fields of relativity and quantum theory.
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## 5. Topological Vector Spaces

1."Topological Vector Spaces (Graduate Texts in Mathematics)" by H H Schaefer and M P Wolff
“Topological Vector Spaces (Graduate Texts in Mathematics)” Book Review: This book is a study of topological vector spaces that assumes familiarity with the elements of general topology and linear algebra. Each chapter begins with an introduction and ends with exercises, including examples and counterexamples with hints where needed. The latest edition includes a new chapter on C^* and W^* algebras, making it an even more valuable resource for students and researchers in the field.
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2."Topological Vector Spaces I (Grundlehren der mathematischen Wissenschaften)" by D J H Garling and Gottfried Köthe
“Topological Vector Spaces I (Grundlehren der mathematischen Wissenschaften)” Book Review: The objective of this book is to provide treatment of the essential concepts, techniques, and outcomes of topological vector space theory. The book presents the fundamental notions of general topology and delves into infinite-dimensional linear algebra in great detail. The concept of a dual pair and linear topologies on vector spaces over arbitrary fields are introduced in a natural way. It features chapters that emphasize the study of real and complex topological vector spaces.
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3."Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity (Dover Books on Mathematics)" by Claude Berge
“Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity (Dover Books on Mathematics)” Book Review: This book focuses on set topology, which studies sets in both topological and topological vector spaces. It provides a systematic development of the properties of multi-valued functions, covering topics such as families of sets, mappings between sets, ordered sets, topological spaces, topological properties of metric spaces, mappings between topological spaces, mappings between vector spaces, convex sets and convex functions in R^n, and topological vector spaces.
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4."Counterexamples in Topological Vector Spaces (Lecture Notes in Mathematics)" by S M Khaleelulla | |

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5."Topological Vector Spaces: The Theory Without Convexity Conditions (Lecture Notes in Mathematics)" by Norbert Adasch and Bruno Ernst | |

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6."Summer School on Topological Vector Spaces (Lecture Notes in Mathematics)" by L Waelbroeck | |

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7."Topological Vector Spaces and Algebras (Lecture Notes in Mathematics)" by Lucien Waelbroeck | |

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8."The Open Mapping and Closed Graph Theorems in Topological Vector Spaces" by Taqdir Husain
“The Open Mapping and Closed Graph Theorems in Topological Vector Spaces” Book Review: The book provides an in-depth understanding of three profound results in functional analysis, namely the open-mapping theorem, the closed-graph theorem, and the Krein-Milman theorem. It covers fundamental concepts and well-established results pertaining to topological and vector spaces. The material is presented in a concise manner, highlighting the key ideas and results commonly used in the field. The book offers a thorough examination of the open-mapping and closed-graph theorems, as well as the Krein-Milman theorem.
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9."Topological Vector Spaces II: 2 (Grundlehren der mathematischen Wissenschaften)" by Gottfried Köthe | |

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10."Analysis in Vector Spaces: Solutions Manual" by Mustafa A Akcoglu and Paul F A Bartha
“Analysis in Vector Spaces: Solutions Manual” Book Review: This book is an introduction to calculus in vector spaces, covering major topics such as sets and functions, real numbers, vector functions, normed vector spaces, and derivatives. It also covers diffeomorphisms and manifolds, higher-order derivatives, multiple integrals, and integration on modules. Graphs and equations are explained in detail, and numerous examples are included for students to practice. This book is suitable for students studying mathematics, physics, computer science, and engineering.
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11."An Introduction to Topology and Modern Analysis" by G F Simmons | |

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## 6. Algebraic Topology

1."Introduction to Functional Analysis" by A Taylor and D Lay
“Introduction to Functional Analysis” Book Review: The book presents a well-organized study of normed linear spaces and linear mappings, serving as a fundamental basis for further exploration in various areas of analysis. Its chapters cover a range of topics, including Banach algebras, weak topologies and duality, equicontinuity, the Krein-Milman theorem, and the theory of Fredholm operators. In addition, it addresses challenges encountered in linear algebra, classical analysis, and differential and integral equations.
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2."Collectively Compact Operator Approximation Theory" by P M Anselone | |

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3."Introduction to Functional Analysis" by A H Siddiqi
“Introduction to Functional Analysis” Book Review: The aim of this book is to cover the major aspects and key topics of functional analysis. Its chapters systematically present basic theorems on properties of functionals and operators, including the Hahn-Banach theorem, Banach-Steinhaus theorem, Open mapping theorem, and Closed graph theorem. The book also explores the practical applications of functional analysis in areas such as operator equations, boundary value problems, optimization, variational inequalities, finite element methods, optimal control, and wavelets. This text is a valuable resource for students and professionals seeking in-depth knowledge of functional analysis.
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4."Algebraic Topology" by Allen Hatcher
“Algebraic Topology” Book Review: This book is designed for students, researchers, professionals, and engineers who are interested in learning about algebraic topology. It covers all the essential concepts of algebraic topology, making it an excellent option for self-study. The chapters of the book cover the main topics of fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory. The material in this book is accompanied by numerous examples and exercises. It will be an invaluable resource for students and teachers alike.
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5."Algebraic Topology: A First Course" by William Fulton
“Algebraic Topology: A First Course” Book Review: This book covers significant concepts and topics of algebraic topology and their applications in diverse mathematical fields. The chapters of this book discuss the connection between homology and integration, Riemann surfaces, winding numbers, degrees of mappings, fixed-point theorems, and plane domains. It also includes various applications of algebraic topology, such as the Jordan curve theorem and the invariance of domain. This book will prove helpful to students and researchers in mathematics and science.
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6."Algebraic Topology" by C R F Maunder
“Algebraic Topology” Book Review: The book focuses on presenting basic algebraic topology from a homotopy theoretical perspective. The chapters cover the construction of homology or homotopy groups of a topological space, homotopy theory, CW-complexes, and cohomology groups associated with a general Ω-spectrum. The book highlights the applications of algebraic topology to various topological problems, such as the classification of surfaces and duality theorems for manifolds. To facilitate the reader’s understanding, numerous examples and exercises are included in this text. This book will be valuable for undergraduate and first-year graduate students studying homotopy or homology theory.
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7."Algebraic Topology" by Robert M Switzer
“Algebraic Topology” Book Review: The aim of this book is to cover the essential concepts and topics of algebraic topology, and to demonstrate their applications in different mathematical fields. The chapters provide an in-depth discussion of important topics, such as the relationship between homology and integration, Riemann surfaces, winding numbers, degrees of mappings, fixed-point theorems, and plane domains. It covers several applications of algebraic topology, including the Jordan curve theorem and the invariance of domain. This book includes various examples and exercises to help readers better understand the material. It will prove useful to both students and researchers in mathematics and science.
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8."A Concise Course in Algebraic Topology" by J P May
“A Concise Course in Algebraic Topology” Book Review: This book is designed for advanced graduate students and teachers of mathematics who seek in-depth knowledge of algebraic topology. The well-structured and self-contained chapters cover a wide range of topics in algebraic topology, while the later section provides sketches of significant areas of the field. The book also showcases the applications of algebraic topology in advanced fields such as geometry, topology, differential geometry, algebraic geometry, and Lie groups. The book offers numerous problems for readers to work on.
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9."Basic Algebraic Topology" by Anant R Shastri
“Basic Algebraic Topology” Book Review: The book provides in-depth knowledge on real analysis, point-set topology, and basic algebra, and is divided into three sections: an introduction to algebraic topology, cell complexes and simplicial complexes, and covering spaces and fundamental groups. The text extensively covers topics such as Poincaré duality, De Rham theorem, cohomology of sheaves, Čech cohomology, higher homotopy groups, Hurewicz’s isomorphism theorem, obstruction theory, Eilenberg-MacLane spaces, and Moore-Postnikov decomposition. The book includes numerous exercises and applications of algebraic topology. It is suitable for graduate students, researchers, and working mathematicians in the field of algebraic topology.
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10."Elements of Algebraic Topology" by James R Munkres
“Elements of Algebraic Topology” Book Review: The purpose of this book is to establish a firm understanding of algebraic topology for readers. The chapters are presented in an accessible and self-contained manner, providing detailed explanations of homology and cohomology theories, universal coefficient theorems, Kunneth theorem, and duality in manifolds. The book also highlights the applications of algebraic topology in classical theorems of point-set topology. For beginners in the field of algebraic topology, this book will be an excellent source of information as it efficiently explains complex and advanced topics.
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