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Basic Topology

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Author : M.A. Armstrong
Publisher : Springer Science & Business Media
ISBN 13 : 1475717938
Total Pages : 260 pages
Book Rating : 4.4/5 (757 download)

Book Synopsis Basic Topology by : M.A. Armstrong

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.

Basic Topology 3

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Author : Mahima Ranjan Adhikari
Publisher : Springer Nature
ISBN 13 : 9811665508
Total Pages : 488 pages
Book Rating : 4.8/5 (116 download)

Book Synopsis Basic Topology 3 by : Mahima Ranjan Adhikari

Download or read book Basic Topology 3 written by Mahima Ranjan Adhikari and published by Springer Nature. This book was released on 2023-03-15 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.

Basic Topology

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Author : M. A. Armstrong
Publisher :
ISBN 13 : 9781475717945
Total Pages : 272 pages
Book Rating : 4.7/5 (179 download)

Book Synopsis Basic Topology by : M. A. Armstrong

Download or read book Basic Topology written by M. A. Armstrong and published by . This book was released on 2014-01-15 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Basic Topology 1

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Author : Avishek Adhikari
Publisher : Springer Nature
ISBN 13 : 9811665095
Total Pages : 523 pages
Book Rating : 4.8/5 (116 download)

Book Synopsis Basic Topology 1 by : Avishek Adhikari

Download or read book Basic Topology 1 written by Avishek Adhikari and published by Springer Nature. This book was released on 2022-07-04 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone–Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand–Kolmogoroff theorem. The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the concepts leading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.

Basic Topology 3

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Author : Mahima Ranjan Adhikari
Publisher :
ISBN 13 : 9789811665516
Total Pages : 0 pages
Book Rating : 4.6/5 (655 download)

Book Synopsis Basic Topology 3 by : Mahima Ranjan Adhikari

Download or read book Basic Topology 3 written by Mahima Ranjan Adhikari and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.

Introduction to Topology

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Author : Bert Mendelson
Publisher : Courier Corporation
ISBN 13 : 0486135098
Total Pages : 226 pages
Book Rating : 4.4/5 (861 download)

Book Synopsis Introduction to Topology by : Bert Mendelson

Download or read book Introduction to Topology written by Bert Mendelson and published by Courier Corporation. This book was released on 2012-04-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

Topology

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Author : Tai-Danae Bradley
Publisher : MIT Press
ISBN 13 : 0262359626
Total Pages : 167 pages
Book Rating : 4.2/5 (623 download)

Book Synopsis Topology by : Tai-Danae Bradley

Download or read book Topology written by Tai-Danae Bradley and published by MIT Press. This book was released on 2020-08-18 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.

Modern General Topology

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Author : Jun-Iti Nagata
Publisher : Elsevier
ISBN 13 : 1483278166
Total Pages : 376 pages
Book Rating : 4.4/5 (832 download)

Book Synopsis Modern General Topology by : Jun-Iti Nagata

Download or read book Modern General Topology written by Jun-Iti Nagata and published by Elsevier. This book was released on 2014-05-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VII: Modern General Topology focuses on the processes, operations, principles, and approaches employed in pure and applied mathematics, including spaces, cardinal and ordinal numbers, and mappings. The publication first elaborates on set, cardinal and ordinal numbers, basic concepts in topological spaces, and various topological spaces. Discussions focus on metric space, axioms of countability, compact space and paracompact space, normal space and fully normal space, subspace, product space, quotient space, and inverse limit space, convergence, mapping, and open basis and neighborhood basis. The book then ponders on compact spaces and related topics, as well as product of compact spaces, compactification, extensions of the concept of compactness, and compact space and the lattice of continuous functions. The manuscript tackles paracompact spaces and related topics, metrizable spaces and related topics, and topics related to mappings. Topics include metric space, paracompact space, and continuous mapping, theory of inverse limit space, theory of selection, mapping space, imbedding, metrizability, uniform space, countably paracompact space, and modifications of the concept of paracompactness. The book is a valuable source of data for mathematicians and researchers interested in modern general topology.

Introduction to Topology

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Author : Theodore W. Gamelin
Publisher : Courier Corporation
ISBN 13 : 0486320189
Total Pages : 258 pages
Book Rating : 4.4/5 (863 download)

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.

Essential Topology

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Author : Martin D. Crossley
Publisher : Springer Science & Business Media
ISBN 13 : 9781852337827
Total Pages : 244 pages
Book Rating : 4.3/5 (378 download)

Book Synopsis Essential Topology by : Martin D. Crossley

Download or read book Essential Topology written by Martin D. Crossley and published by Springer Science & Business Media. This book was released on 2011-02-11 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.

Topology

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Author : Marco Manetti
Publisher : Springer
ISBN 13 : 3319169580
Total Pages : 309 pages
Book Rating : 4.3/5 (191 download)

Book Synopsis Topology by : Marco Manetti

Download or read book Topology written by Marco Manetti and published by Springer. This book was released on 2015-06-19 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

General Topology I

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Author : A.V. Arkhangel'skii
Publisher : Springer Science & Business Media
ISBN 13 : 3642612652
Total Pages : 210 pages
Book Rating : 4.6/5 (426 download)

Book Synopsis General Topology I by : A.V. Arkhangel'skii

Download or read book General Topology I written by A.V. Arkhangel'skii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of the encyclopaedia volumes devoted to general topology. It has two parts. The first outlines the basic concepts and constructions of general topology, including several topics which have not previously been covered in English language texts. The second part presents a survey of dimension theory, from the very beginnings to the most important recent developments. The principal ideas and methods are treated in detail, and the main results are provided with sketches of proofs. The authors have suceeded admirably in the difficult task of writing a book which will not only be accessible to the general scientist and the undergraduate, but will also appeal to the professional mathematician. The authors' efforts to detail the relationship between more specialized topics and the central themes of topology give the book a broad scholarly appeal which far transcends narrow disciplinary lines.

Basic Modern Algebra with Applications

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Author : Mahima Ranjan Adhikari
Publisher : Springer Science & Business Media
ISBN 13 : 8132215990
Total Pages : 650 pages
Book Rating : 4.1/5 (322 download)

Book Synopsis Basic Modern Algebra with Applications by : Mahima Ranjan Adhikari

Download or read book Basic Modern Algebra with Applications written by Mahima Ranjan Adhikari and published by Springer Science & Business Media. This book was released on 2013-12-08 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.

Lectures on the Topology of 3-manifolds

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Author : Nikolai Saveliev
Publisher : Walter de Gruyter
ISBN 13 : 9783110162721
Total Pages : 220 pages
Book Rating : 4.1/5 (627 download)

Book Synopsis Lectures on the Topology of 3-manifolds by : Nikolai Saveliev

Download or read book Lectures on the Topology of 3-manifolds written by Nikolai Saveliev and published by Walter de Gruyter. This book was released on 1999 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Basic Course in Algebraic Topology

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Author : William S. Massey
Publisher : Springer
ISBN 13 : 1493990632
Total Pages : 448 pages
Book Rating : 4.4/5 (939 download)

Book Synopsis A Basic Course in Algebraic Topology by : William S. Massey

Download or read book A Basic Course in Algebraic Topology written by William S. Massey and published by Springer. This book was released on 2019-06-28 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.

Basic Algebraic Topology and its Applications

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Author : Mahima Ranjan Adhikari
Publisher : Springer
ISBN 13 : 813222843X
Total Pages : 615 pages
Book Rating : 4.1/5 (322 download)

Book Synopsis Basic Algebraic Topology and its Applications by : Mahima Ranjan Adhikari

Download or read book Basic Algebraic Topology and its Applications written by Mahima Ranjan Adhikari and published by Springer. This book was released on 2016-09-16 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Cape Cod

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Author : Henry David Thoreau
Publisher :
ISBN 13 :
Total Pages : 270 pages
Book Rating : 4.:/5 (32 download)

Book Synopsis Cape Cod by : Henry David Thoreau

Download or read book Cape Cod written by Henry David Thoreau and published by . This book was released on 1892 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: