57 Best Books on General Topology

“General Topology” Book Review: The book reflects deep and systematic information on general topology. The chapters of this book are well-structured, precise, and to-the-point. It provides a strong base for dealing with modern analysis. It consists of several problems for self-assessment and practice of the readers. The final section of the book presents an axiomatic treatment of set theory. For better understanding of the readers many counterexamples and applications of general topology in different fields are highlighted in this text. The book will be an asset for mathematicians working in the field of analysis.

“General Topology” Book Review: The book is an updated and revised piece of work featuring latest topics and recent developments in the field of general topology. The chapters of this book are reader-friendly and describe each topic uniquely and efficiently. Many important definitions and theorems of general topology are included in this book. The topics featured in this book are clearly explained and elaborated with the help of suitable examples. The book consists of numerous solved problems and practice exercises. For providing better practical knowledge and relatable content to the readers many practices and applications of general topology are highlighted. The book will be beneficial for the students of mathematics.

“General Topology” Book Review: The book broadly covers two major areas of general topology that are, continuous topology and geometric topology. The chapters of this book present all the major topics of set theory, metric spaces, topological spaces, new spaces from old, convergence, separation and countability, compactness, metrizable spaces, connectedness, uniform spaces, and function spaces. The topics connectivity properties, topological characterization theorems, and homotopy theory are clearly highlighted in this text. The book will be useful for the advanced undergraduate students of mathematics, generally dealing with general topology. Under continuous topology, the book covers convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces in great detail. The book also introduces many standard spaces for each related problem in every section. Numerous diagrams, examples, historical notes, a bibliography, and index are also included. This book is intended for advanced undergraduate and beginning graduate students.

“General Topology” Book Review: The book is a well-structured and organized piece of writing featuring major aspects and essential concepts of general topology. The topics like topological spaces, Moore-Smith convergence, product and quotient spaces, embedding and metrization, and compact, uniform, and function spaces are thoroughly explained. The book is enriched with several examples, problems, and theorems. The applications of general topology in various fields of mathematics are mentioned in this book. It will provide an essential foundation for modern analysis. The book will be valuable for graduating students of mathematics and sciences.

“Schaum’s Outline of General Topology” Book Review: The book aims at presenting the specialized topics of topology. The chapters of this book are comprehensive, precise, and explain each concept in proper steps. The technique of effective problem-solving is introduced in this text. The content of this book is supported by many solved and unsolved problems. It will be a great source of information as the topics featured in this book are reviewed by the experts in their respective fields. The applications of general topology in various fields are mentioned in this text. The book will be suitable for the undergraduate and graduate courses in general topology.

“Introduction to Topology” Book Review: The book provides an ideal introduction to the basic principles and concepts of topology. It begins with a clear description of set theory. The chapters of this book are majorly based on metric spaces, topological spaces, connectedness, and compactness. The book is an easy-to-understand writing featuring important definitions and proofs of theorems. It consists of several exercises for self-study and practice of the readers. The book will be a good resource of the under-graduating and graduating students of mathematics seeking deep knowledge in calculus.

“General Topology” Book Review: The book focuses on a clear presentation of fundamental concepts of topology. The theory of real-valued functions of a real variable is illustrated in this text. The topics like uniform continuity, uniform convergence, equicontinuity, and Bolzano-Weierstrass theorem are described in detail. To give the book’s content visual support many figures are included in this book. To give better practical knowledge and relatable content to the readers several worked examples and applications are presented. The book will be beneficial for the under-graduating and graduating students of mathematics.

“General Topology” Book Review: The book presents all the basic concepts, definitions, and principles of general topology. The uniform structures, topological spaces, and real numbers along with their properties are addressed in this book. The chapters of this book describe all the major topics related to Haar measure, convolution and representations, and measures on Hausdorff topological spaces. Each chapter ends with a bunch of exercises. The featured topics and concepts are clearly explained with the help of suitable examples. The applications of general topology in various fields are highlighted in this piece of work. The student of mathematics related to topology will find this book valuable.

“Principles of Topology” Book Review: The book aims at presenting general topology from a geometrical perspective. The initial section of the book describes metric spaces, general topological spaces, continuity, topological equivalence, basis, subbasis, connectedness, compactness, separation properties, and metrization. The later section covers subspaces, product spaces, and quotient spaces. In addition, the text introduces geometric, differential, and algebraic topology. For self-study and self-assessment of the readers, the book consists of numerous exercises. The applications of topological ideas and concepts in geometry as well as mathematical analysis are highlighted. The book will be a great source of information for the undergraduate and graduate students of mathematics involved in topology and multivariable calculus.

“General Topology” Book Review: This book develops basic metric topological methods and algebraic needs. It introduces the vector character of Euclidean n-space and familiar facts from linear algebra. It also covers concepts relevant to convex body theory and the affine character of the space. The analogy between linear and affine concepts are also explained. It covers methods on how to verify intuitive relations analytically in space of general dimensions. Also contains a collection of standard fundamental theorems.

“Topology” Book Review: The book explores the concept of topology in two parts. Part I is dedicated to set theory and the fundamentals of topology. These concepts are utilized while exploring point-set or set-theoretic topology, algebraic topology, functional analysis, continuum theory, etc. in Part II. The book is suitable for advanced undergraduate and beginning graduate students studying introductory courses in topology.

“Topology” Book Review: This book offers a detailed treatment of both general topology and algebraic topology. Their various applications in the real world are also explored. Numerous illustrations, examples and problems are provided to help readers have a better understanding of the subject matter.

“Topology” Book Review: The book introduces elementary set theory, ordinals and cardinals, topological spaces, Cartesian products, and connectedness in the first few chapters. This is followed by an explanation of identification topology, weak topology, separation axioms, covering axioms, metric spaces, and convergence. The book also deals with compactness, function spaces, the spaces C(Y), complete spaces, and homotopy in great detail. Subsequent chapters describe maps into spheres, topology of En, homotopy type, path spaces, H-spaces, and fiber spaces.

“Introduction to Topology and Modern Analysis” Book Review: This book extensively covers the mathematical aspects of continuity and linearity. After explaining their basic definition, the book explores their relationship to each other in terms of topology and modern analysis. Students, researchers, and professionals can refer to this book.

“Topology” Book Review: This book explores the fundamental aspects and applications of the vast field of topology in the real world. Both the algebraic topology and general topology are covered in detail. Replete with examples, figures, and exercises, this book is ideal for postgraduate and honors students in Indian universities.

“Topology: A Geometric Approach” Book Review: This book deals with the metric spaces which include normed linear spaces and inner product spaces. This book is written in a student-friendly manner. This book is helpful for postgraduate level students. Many worked out examples and problems have been included in this book. Concepts are illustrated using figures for enhancing understanding. Certain additional topics are given in appendices at the end of each chapter for more information. The book explores the affine, projective, and Euclidean geometries of topology with added focus on normed linear spaces, inner product spaces as well as both finite and infinite dimensional metric spaces. The text is provided in a concise and lucid manner using plenty of appendices, diagrams, solved examples, and problems. Postgraduate students can refer to this book.

“Topology of Metric Spaces” Book Review: This book is useful for studying the higher aspects of topology and analysis. Theorems are explained with proofs with real world examples. It also contains numerical problems and solutions to them. This book is written for undergraduate students. This book builds a foundation by which one can relate to real world application. This book streamlines the fundamentals of metric space topology using concrete spaces and geometric ideas to enhance geometric thinking skill. This book also deals with real analysis and encourages readers to study about modern analysis. Numerous concrete examples of spaces and maps are provided. This makes it an ideal reference book to study general topology or point-set topology. Students and professionals may refer to this book.

“Introduction to Topology: Pure and Applied” Book Review: This book introduces topology which is an important mathematics discipline. This book adopts a mathematical approach to explain the fundamentals of topology and its applications to other fields like economics, science, engineering, and mathematics. The book begins with the basics of point-set topology. A description of the basics of point-set topology is followed by an in-depth discussion on knots, robotics and graphs. Undergraduate students can refer to this book. It contains illustrations based on real-world applications. The book covers topics like knots, robotics and graphs. It describes the importance of the application of topology to other fields.

“Topology” Book Review: This book presents the fundamental principles, techniques and theorems encompassing the vast field of topology. Topics such as Kuratowski closure operator, separation axioms, connectedness, compactness, and paracompactness are introduced initially. The book also addresses important results of the Tychonoff theorem, the Tietze extension theorem, the Urysohn metrization theorem, the Stone theorem. Subsequent chapters deal with homotopy, metrizability and bitopological spaces.

“Topology and Geometry in Physics” Book Review: This book presents the modern applications and recent developments in the fields of physical research. It provides an introduction to topological concepts in supersymmetric solitons, gauge theories, chiral anomalies, BRST quantization, and noncommutative geometry. Written as a set of extensive lectures, this book is recommended for novices to the field, postgraduate students, and lecturers requiring advanced material.

“Modern Geometry Methods and applications-II” Book Review: This book offers an excellent overview of the key theories and outlook of the topic. The book covers the topic in deeper detail than the general topic. This book is written in a student-friendly style and teaches real subjects. The book deals with topics like elasticity, relativity, the theory of tensors, covariant differentiation, Riemannian curvature, geodesics and the calculus of variations, conservation laws and Hamiltonian formalism, skew-symmetric tensors etc.

“Differential Topology” Book Review: This book determines the latest view of the topic and its functional analysis with its numerous relations to other branches of mathematics. The book guides the reader step by step throughout the proofs. This book covers the topic well requiring only undergraduate analysis and linear algebra and covers the topics like Manifolds and smooth maps, Transversality and intersection, Oriented intersection theory, Integration on manifolds and sub topics like Derivatives and tangents, transversality, homotopy & stability, the borsuk ulam theorem, lefschetz fixed point theory, the hopf degree theorem, exterior algebra, exterior derivative, appendix-1 & 2 as Measure Zero and Sard’s theorem & Classification of Compact One-Manifolds. This book is suitable for introductory graduate courses or an advanced undergraduate course.

“Differential Topology” Book Review: The book starts with the most basic idea and properties of the subject. The topics are well designed and well structured and the proofs are clear. This book is very readable and approachable & the prerequisites are very minimum. The book covers the topics like Manifolds and Maps, Function Spaces, Transversality, Vector Bundles and Tubular Neighborhoods, Degrees, Intersection Numbers, and the Euler Characteristic, Morse Theory, Cobordism, Isotopy, Surfaces, etc.and some appendices which briefly summarizes some of the background material. It has numerous examples on the theories used along with some motivating examples ranging in difficulty from the routine to the unsolved and providing examples and further developments of the theory.

“Elements of Differential Topology” Book Review: This book describes the topics in an elegant way. The book begins with differential and integral calculus and leads the reader through the intricacies of manifold theory along with discussion on algebraic topology, algebraic/differential geometry, and Lie groups. The book reviews differential and integral calculus and presents the results which can be used throughout. The exercises are included along with their solutions at the end of all the chapters. This book covers topics like Review of Differential Calculus, Integral Calculus, Submanifolds of Euclidean Spaces, Integration on Manifolds, Abstract Manifolds, Isotopy, Intersection Theory, Geometry of Manifolds, Lie Groups and Lie Algebras, etc.

“Elements of Topological Dynamics” Book Review: The book is an introduction on the topic. Here the reader studies the topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equations. This book reflects the choice and organisation of the material both elementary and basic which is sufficient to understand recent research papers in this field. This book has a systematic exposition of the fundamental methods and techniques of abstract Subject. The book covers topics like Various Aspects of the Theory of Dynamical Systems, Continuous and Discrete Flows, Important Examples, The General Framework, Equicontinuity and Distality, Structure of Extensions, etc. This book gives a better view of methods and techniques rather than a discussion of the leading problems and their solutions.

“Elements of the Theory of Functions and Functional Analysis” Book Review: This book is thoroughly updated and is streamlined to reflect the upliftment in the field. This book is dynamic and has an engaging style. The coves topics like fundamental of Set theory, Metric spaces, Normed linear spaces, The concept of cardinal numbers, Partition into classes, Mapping of sets, General concept of function, Weak convergence, Open and closed sets, Complete metric spaces are explained with examples in detail. It also covers some important topics like Linear Operators, Linear Operator Equations Fredholms Theorems, Real functions in metric spaces, Linear Operator Equations Fredholms Theorems, Fubini’s theorem, Products of sets and measures etc.

“Differential Topology” Book Review: This book determines the latest view of the topic and its functional analysis with its numerous relations to other branches of mathematics. The book guides the reader step by step throughout the proofs. This book covers the topic well requiring only undergraduate analysis and linear algebra and covers the topics like Manifolds and smooth maps, Transversality and intersection, Oriented intersection theory, Integration on manifolds and sub topics like Derivatives and tangents, transversality, homotopy & stability, the borsuk ulam theorem, lefschetz fixed point theory, the hopf degree theorem, exterior algebra, exterior derivative, appendix-1 & 2 as Measure Zero and Sard’s theorem & Classification of Compact One-Manifolds. This book is suitable for introductory graduate courses or an advanced undergraduate course.

“Differential Topology: First Steps” Book Review: The book stimulates students intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. In this book, the course has been made more accessible and useful. This book goes from the elementary level and easily catches up with advanced topics along with covering all the standard topics. The book mainly focuses on methods of spherical modifications and the study of critical points of functions on manifolds. This book offers introductory material regarding all the topics it covers, so the book does not require any prerequisite. The book covers topics like Set Theoretic Symbols, Topological Spaces, Open and Closed Sets, Topological Products, Continuous Maps, A Theorem on 3-Manifolds, The Non Orientable Case, Two-Dimensional Manifolds, Rearrangement of Modifications, Definition of Modifications, Spherical Modifications, Cobounding Manifolds, Displacement and Isotopy, Interpretation of Theorem 6-5 in Terms of Critical Points, etc.

“Differential Topology” Book Review: This book helps in exploring the Scope of the topic. This book offers a wide perspective on the field through its comprehensive account of geometric techniques for studying the topology of smooth manifolds. In this book the concepts of manifold are introduced from the first principle, which is supplemented thorough appendices giving background on topology and homotopy theory. This book derives deep results from the foundation by giving a thorough and deep treatment of general position and transversality, proper actions of Lie groups, immersions and embeddings, concluding with the surgery procedure and cobordism theory. This book is well explained and rigorous in its approach with a growing complexity on different levels. The reader must have a little knowledge of the subject book approaching. This book gives advanced students and researchers an accessible route into the field of differential topology.

“Introduction to Differential Topology” Book Review: This book offers an excellent overview of the key theories and outlook of the topic. The context here is wrapped up with simple words and with a detailed understanding of all the key topics. The book is an elementary introduction to differential manifolds. The book concentrates on geometric aspects and explains not only the basic properties but also teaches how to do the basic geometrical constructions. The book has many diagrams which illustrate the proofs and is supplied with enormous problems. The reader must have a basic knowledge on analysis and topology. The book covers topics like Manifolds and differentiable structures, Tangent space, Vector bundles, Linear algebra for vector bundles, Local and tangential properties, Sard’s theorem, Embedding, Dynamical systems, Isotopy of embeddings, Connected sums, Second order differential equations and sprays, The exponential map and tubular neighbourhoods, Manifolds with boundary, Transversality, etc.

“Topology and Geometry for Physicists (Dover Books on Mathematics)” Book Review: This text provides an introduction to geometrical and topological methods in theoretical physics and applied mathematics. No detailed background in topology or geometry is required. The book focuses on physical motivations, that enables the students to apply the techniques to their physics formulas and research. The physics applications of the book range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection, covariant derivatives and Morse theory.

“Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists” Book Review: This book provides a complete and detailed coverage of the essentials of modern differential geometry and topology. It covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy and de Rham cohomology. In addition, the book includes detailed exercises for the students to test their understanding. It also includes applications that show fundamental connections to classical mechanics, electromagnetism (including circuit theory), general relativity and gauge theory. The book is useful for undergraduate and graduate students in mathematics and the physical sciences.

“Topology for Physicists (Grundlehren der mathematischen Wissenschaften)” Book Review: This book is a detailed study of the subject of topology. It describes the use of topology in the quantum field theory. It shows how topological nontrivial solutions of the classical equations of motion (solitons and instantons) allow the physicist to leave the framework of perturbation theory. It covers important applications of topology in other areas of physics such as the study of defects in condensed media, singularities in the excitation spectrum of crystals. It provides a detailed coverage of the basic concepts of topology that is essential to quantum field theorists. Homotopy theory, homology theory and fibration theory are also covered. The book is useful for physicists and researchers working in the field of topology.

“Differential Manifolds: A Basic Approach For Experimental Physicists” Book Review: This book provides description of the basics of differential manifolds with a full proof of any element. The book mainly focuses on the basic mathematical concepts. It covers all the essential topics required for the development of the differential manifolds. This book starts from first principles. The mathematical framework is the set theory with its axioms and its formal logic. No special knowledge is needed. The book is important for all research physicists to gain a firm grounding in the field. It will also benefit experimental physicists to manipulate equations and expressions in that framework.

“Geometric Algebra for Physicists” Book Review: This book provides the latest information on geometric algebra. It begins by providing a detailed introduction to geometric algebra. It covers numerous topics- new techniques for handling rotations in arbitrary dimensions, the links between rotations, bivectors and the structure of the Lie groups. Then it goes on to include the concept of a complex analytic function theory to arbitrary dimensions, with applications in quantum theory and electromagnetism. Applications such as black holes and cosmic strings are also explored. It can be used as a graduate text for courses on the physical applications of geometric algebra. The book will also be suitable for researchers working in the fields of relativity and quantum theory.

“Topological Vector Spaces (Graduate Texts in Mathematics)” Book Review: The book is on topological vector spaces. It talks about the familiarity with the elements of general topology and linear algebra. The chapters of the book start with introduction and ends with exercises. The book has examples and counterexamples and has hints where it is needed. It contains new chapter on C^* and W^* algebras.

“Topological Vector Spaces I (Grundlehren der mathematischen Wissenschaften)” Book Review: The book aims to give a systematic account of the most important ideas, methods and results of the theory of topological vector spaces. The book gives the fundamental ideas of general topology. It discusses infinite dimensional linear algebra in detail. Concept of dual pair and linear topologies on vector spaces over arbitrary fields are given in a natural manner. It contains chapters which stress on real and complex topological vector spaces.

“Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity (Dover Books on Mathematics)” Book Review: The book is on set topology, which studies sets in topological spaces and topological vector spaces. The book has a systematic development of the properties of multi-valued functions. It includes topics like families of sets, mappings of one set into another, ordered sets, topological spaces, topological properties of metric spaces, mappings from one topological space into another, mappings of one vector space into another, convex sets and convex functions in the space R” and topological vector spaces.

“The Open Mapping and Closed Graph Theorems in Topological Vector Spaces” Book Review: The book tells about the understanding of three of the deepest results of Functional Analysis, the open-mapping and closed­ graph theorems, and the so-called Krein-~mulian theorem. It contains important notions and well known results about topological and vector spaces. The book presents the material to give a quick resume of the result and the ideas that are commonly used in the field. It contains a detailed study of the open-mapping and closed-graph theorems as well as the Krein-~mulian theorem.

“Analysis in Vector Spaces: Solutions Manual” Book Review: This book provides the introduction to calculus in vector spaces. Major chapters introduced are sets and functions, real numbers, vector functions, normed vector spaces and derivatives. Other topics mentioned are diffeomorphisms and manifolds, higher-order derivatives, multiple integrals and integration on modules. Graphs and equations are discussed in a detailed manner. Examples are added for students’ practice. This book can be used by students studying mathematics, physics, computer science and engineering.

“Introduction to Functional Analysis” Book Review: The book is a well-structured and self-contained piece of writing featuring the theory of normed linear spaces and of linear mappings. It aims in providing the essential base for further study in many areas of analysis. The chapters based on Banach algebras, material on weak topologies and duality, equicontinuity, Krein-Milman theorem, and theory of Fredholm operators are included in this book. The book also highlights the problems faced in linear algebra, classical analysis, and differential and integral equations.

“Introduction to Functional Analysis” Book Review: The book aims at presenting the major aspects and important topics of functional analysis. The chapters of this book reflect basic theorems dealing with properties of functional and operators namely, Hahn-Banach theorem, Banach-Steinhaus theorem, Open mapping theorem and Closed graph theorem. The book also highlights the applications of functional analysis in operator equations, boundary value problems, optimization, variational inequalities, finite element methods, optimal control, and wavelets. The students and professionals seeking deep information in functional analysis will find this text helpful.

“Algebraic Topology” Book Review: The book delicately focuses students, researchers, professionals, engineers in the development of algebraic topology. All the basic concepts of algebraic topology are covered in this text, hence making it an ideal choice for self-study. The chapters of this book cover all the major topics of fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory. The content of this book is supported with many examples and exercises. This book will be useful for students and teachers.

“Algebraic Topology: A First Course” Book Review: The book presents important concepts and topics of algebraic topology along with their applications in various areas of mathematics. The chapters of this book describe topics like relation between homology and integration, plane domains, Riemann surfaces, winding numbers, degrees of mappings, and fixed-point theorems. Various applications of algebraic topology namely, Jordan curve theorem and invariance of domain are included in this text. The book will be beneficial for the students of mathematics and science.

“Algebraic Topology” Book Review: The book aims at presenting basic algebraic topology from a homotopy theoretical point-of-view. The chapters of this book feature construction homology or homotopy groups of a topological space, homotopy theory, CW-complexes, and co-homology groups associated with a general Ω-spectrum. The applications of algebraic topology to various topological problems such as classification of surfaces and duality theorems for manifolds are highlighted in this book. For better understanding of the readers many examples and exercises are included in this text. The book will be valuable for the undergraduate and first-year graduate students of related to homotopy or homology theory.

“Algebraic Topology” Book Review: The book is a contemporary piece of writing presenting the latest topics and untouched aspects of homotopy and homology. The chapters of this book are comprehensive, precise, and revolve around homotopy groups of sphere and computation of various cobordism groups. The stable homotopy theory is featured in this book along with its basic concepts, principle methods, and applications in different fields. The book will be a good resource for the professionals and experts in the field of algebraic topology.

“A Concise Course in Algebraic Topology” Book Review: The book will be suitable for the teachers and advanced graduate students of mathematics. The chapters of this book are well-structured, self-contained, and deliver deep information on various topics of algebraic topology. The later section of the book portrays the sketches of substantial areas of algebraic topology. The applications of algebraic topology in various advanced fields namely geometry, topology, differential geometry, algebraic geometry and lie groups are highlighted in this piece of writing. The book consists of numerous problems for self-study and self-assessment of the readers.

“Basic Algebraic Topology” Book Review: The book reflects deep information on real analysis, point-set topology, and basic algebra. It is broadly classified into three sections featuring introduction of algebraic topology, cell complexes and simplicial complexes, and covering spaces and fundamental groups, respectively. The Poincaré duality, De Rham theorem, cohomology of sheaves, Čech cohomology is discussed in detail. The topics like higher homotopy groups, Hurewicz’s isomorphism theorem, obstruction theory, Eilenberg-MacLane spaces, and Moore-Postnikov decomposition are thoroughly explained. The content of this book is enriched with several exercises and applications of algebraic topology. The book will be appropriate for the graduate students, researchers, and working mathematicians related to the field of algebraic topology.

“Elements of Algebraic Topology” Book Review: The book aims in providing readers a strong foundation in the field of algebraic topology. The chapters of this book are reader-friendly, self-contained, and contain a detailed description of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, and duality in manifolds. The applications of algebraic topology in the classical theorems of point-set topology are clearly mentioned in this book. The book will be a great source of information for the beginners in algebraic topology, as it explains the complex and advanced topics, quite efficiently.