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Elements Of Topology
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Book Synopsis Elements of Topology by : Tej Bahadur Singh
Download or read book Elements of Topology written by Tej Bahadur Singh and published by CRC Press. This book was released on 2013-05-20 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology is a large subject with many branches broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad variety of mathematical disciplines. Algebraic topology serves as a powerful tool for studying the problems in geometry and numerous other areas of mathematics. Ele
Book Synopsis Elements of Point Set Topology by : John D. Baum
Download or read book Elements of Point Set Topology written by John D. Baum and published by Courier Corporation. This book was released on 1991-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.
Book Synopsis Elementary Concepts of Topology by : Paul Alexandroff
Download or read book Elementary Concepts of Topology written by Paul Alexandroff and published by Courier Corporation. This book was released on 2012-08-13 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.
Book Synopsis Elements of Topological Dynamics by : J. de Vries
Download or read book Elements of Topological Dynamics written by J. de Vries and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa is in the tradition of the books [GH] and [EW. The title tions. So this book (,Elements . . . ' rather than 'Introduction . . . ') does not mean that this book should be compared, either in scope or in (intended) impact, with the 'Ele ments' of Euclid or Bourbaki. Instead, it reflects the choice and organisation of the material in this book: elementary and basic (but sufficient to understand recent research papers in this field). There are still many challenging prob lems waiting for a solution, and especially among general topologists there is a growing interest in this direction. However, the technical inaccessability of many research papers makes it almost impossible for an outsider to under stand what is going on. To a large extent, this inaccessability is caused by the lack of a good and systematic exposition of the fundamental methods and techniques of abstract TO. This book is an attempt to fill this gap. The guiding principle for the organization of the material in this book has been the exposition of methods and techniques rather than a discussion of the leading problems and their solutions. though the latter are certainly not neglected: they are used as a motivation wherever possible.
Book Synopsis Elements of Differential Topology by : Anant R. Shastri
Download or read book Elements of Differential Topology written by Anant R. Shastri and published by CRC Press. This book was released on 2011-03-04 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others. It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topol
Book Synopsis Elements of Homology Theory by : Viktor Vasilʹevich Prasolov
Download or read book Elements of Homology Theory written by Viktor Vasilʹevich Prasolov and published by American Mathematical Soc.. This book was released on 2007 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.
Book Synopsis Elements of Topology by : Tej Bahadur Singh
Download or read book Elements of Topology written by Tej Bahadur Singh and published by CRC Press. This book was released on 2013-05-20 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology is a large subject with many branches broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad variety of mathematical disciplines. Algebraic topology serves as a powerful tool for studying the problems in geometry and numerous other areas of mathematics. Elements of Topology provides a basic introduction to point-set topology and algebraic topology. It is intended for advanced undergraduate and beginning graduate students with working knowledge of analysis and algebra. Topics discussed include the theory of convergence, function spaces, topological transformation groups, fundamental groups, and covering spaces. The author makes the subject accessible by providing more than 250 worked examples and counterexamples with applications. The text also includes numerous end-of-section exercises to put the material into context.
Book Synopsis Basic Elements of Differential Geometry and Topology by : S.P. Novikov
Download or read book Basic Elements of Differential Geometry and Topology written by S.P. Novikov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi ..., si j'avait su comment en revenir, je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Matht"natics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics seNe as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series
Author :O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov Publisher :American Mathematical Soc. ISBN 13 :9780821886250 Total Pages :432 pages Book Rating :4.8/5 (862 download)
Book Synopsis Elementary Topology by : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Download or read book Elementary Topology written by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov and published by American Mathematical Soc.. This book was released on with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.
Book Synopsis Elements of the Topology of Plane Sets of Points by : Maxwell Herman Alexander Newman
Download or read book Elements of the Topology of Plane Sets of Points written by Maxwell Herman Alexander Newman and published by Praeger. This book was released on 1985-09-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an elementary introduction to the ideas and methods of topology by the detailed study of certain topics. There are elegant but rigorous proofs of many of the basic theorems, and special attention is given to the results needed in the theory of functions.
Book Synopsis Elements of Mathematics by : Nicolas Bourbaki
Download or read book Elements of Mathematics written by Nicolas Bourbaki and published by . This book was released on 1966 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis First Concepts of Topology by : William G. Chinn
Download or read book First Concepts of Topology written by William G. Chinn and published by MAA. This book was released on 1966 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 150 problems and solutions.
Book Synopsis Elements of Modern Topology by : Ronald Brown
Download or read book Elements of Modern Topology written by Ronald Brown and published by . This book was released on 1968 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elements Of Algebraic Topology by : James R. Munkres
Download or read book Elements Of Algebraic Topology written by James R. Munkres and published by CRC Press. This book was released on 2018-03-05 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature of algebraic topology for beginners.
Download or read book Basic Topology written by M.A. Armstrong and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties help students gain a thorough understanding of the subject.
Book Synopsis Introduction to Topology by : Theodore W. Gamelin
Download or read book Introduction to Topology written by Theodore W. Gamelin and published by Courier Corporation. This book was released on 2013-04-22 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
Book Synopsis Elements of Homotopy Theory by : George W. Whitehead
Download or read book Elements of Homotopy Theory written by George W. Whitehead and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory. It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal Coefficient and Kiinneth Theorems. Some acquaintance with manifolds and Poincare duality is desirable, but not essential. Anyone who has taught a course in algebraic topology is familiar with the fact that a formidable amount of technical machinery must be introduced and mastered before the simplest applications can be made. This phenomenon is also observable in the more advanced parts of the subject. I have attempted to short-circuit it by making maximal use of elementary methods. This approach entails a leisurely exposition in which brevity and perhaps elegance are sacrificed in favor of concreteness and ease of application. It is my hope that this approach will make homotopy theory accessible to workers in a wide range of other subjects-subjects in which its impact is beginning to be felt. It is a consequence of this approach that the order of development is to a certain extent historical. Indeed, if the order in which the results presented here does not strictly correspond to that in which they were discovered, it nevertheless does correspond to an order in which they might have been discovered had those of us who were working in the area been a little more perspicacious.
