Basic Topology 1

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Basic Topology 1

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

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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

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

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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

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

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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.

General Topology I

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

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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.

The General Topology of Dynamical Systems

Author : Ethan Akin
Publisher : American Mathematical Soc.
ISBN 13 : 0821849328
Total Pages : 273 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The General Topology of Dynamical Systems by : Ethan Akin

Download or read book The General Topology of Dynamical Systems written by Ethan Akin and published by American Mathematical Soc.. This book was released on 1993 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results. This book collects these results, both old and new, and organises them into a natural foundation for all aspects of dynamical systems theory.

Basic Modern Algebra with Applications

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

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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.

Basic Algebraic Topology and its Applications

Author : Mahima Ranjan Adhikari
Publisher : Springer
ISBN 13 : 813222843X
Total Pages : 628 pages
Book Rating : 4.1/5 (322 download)

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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 628 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.

Topology

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

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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.

Basic Concepts of Algebraic Topology

Author : F.H. Croom
Publisher : Springer Science & Business Media
ISBN 13 : 1468494759
Total Pages : 187 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Basic Concepts of Algebraic Topology by : F.H. Croom

Download or read book Basic Concepts of Algebraic Topology written by F.H. Croom and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended as a one semester introduction to algebraic topology at the undergraduate and beginning graduate levels. Basically, it covers simplicial homology theory, the fundamental group, covering spaces, the higher homotopy groups and introductory singular homology theory. The text follows a broad historical outline and uses the proofs of the discoverers of the important theorems when this is consistent with the elementary level of the course. This method of presentation is intended to reduce the abstract nature of algebraic topology to a level that is palatable for the beginning student and to provide motivation and cohesion that are often lacking in abstact treatments. The text emphasizes the geometric approach to algebraic topology and attempts to show the importance of topological concepts by applying them to problems of geometry and analysis. The prerequisites for this course are calculus at the sophomore level, a one semester introduction to the theory of groups, a one semester introduc tion to point-set topology and some familiarity with vector spaces. Outlines of the prerequisite material can be found in the appendices at the end of the text. It is suggested that the reader not spend time initially working on the appendices, but rather that he read from the beginning of the text, referring to the appendices as his memory needs refreshing. The text is designed for use by college juniors of normal intelligence and does not require "mathematical maturity" beyond the junior level.

Elementary Topology

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)

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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.

Topology Through Inquiry

Author : Michael Starbird
Publisher : American Mathematical Soc.
ISBN 13 : 1470462613
Total Pages : 313 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topology Through Inquiry by : Michael Starbird

Download or read book Topology Through Inquiry written by Michael Starbird and published by American Mathematical Soc.. This book was released on 2020-09-10 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning—of mathematics and beyond—joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.

Essential Topology

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

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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.

General Topology

Author : John L. Kelley
Publisher : Courier Dover Publications
ISBN 13 : 0486820661
Total Pages : 321 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis General Topology by : John L. Kelley

Download or read book General Topology written by John L. Kelley and published by Courier Dover Publications. This book was released on 2017-03-07 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive text for beginning graduate-level students and professionals. "The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure." — Bulletin of the American Mathematical Society. 1955 edition.

Introduction to Topology

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

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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.

A Basic Course in Algebraic Topology

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

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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.

General Topology

Author : J. Dixmier
Publisher : Springer Science & Business Media
ISBN 13 : 1475740328
Total Pages : 150 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis General Topology by : J. Dixmier

Download or read book General Topology written by J. Dixmier and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a course in general topology, intended for students in the first year of the second cycle (in other words, students in their third univer sity year). The course was taught during the first semester of the 1979-80 academic year (three hours a week of lecture, four hours a week of guided work). Topology is the study of the notions of limit and continuity and thus is, in principle, very ancient. However, we shall limit ourselves to the origins of the theory since the nineteenth century. One of the sources of topology is the effort to clarify the theory of real-valued functions of a real variable: uniform continuity, uniform convergence, equicontinuity, Bolzano-Weierstrass theorem (this work is historically inseparable from the attempts to define with precision what the real numbers are). Cauchy was one of the pioneers in this direction, but the errors that slip into his work prove how hard it was to isolate the right concepts. Cantor came along a bit later; his researches into trigonometric series led him to study in detail sets of points of R (whence the concepts of open set and closed set in R, which in his work are intermingled with much subtler concepts). The foregoing alone does not justify the very general framework in which this course is set. The fact is that the concepts mentioned above have shown themselves to be useful for objects other than the real numbers.

Introduction to Topology

Author : V. A. Vasilʹev
Publisher : American Mathematical Soc.
ISBN 13 : 0821821628
Total Pages : 165 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Topology by : V. A. Vasilʹev

Download or read book Introduction to Topology written by V. A. Vasilʹev and published by American Mathematical Soc.. This book was released on 2001 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, homology and cohomology, intersection index, etc. The author notes, "The lecture note origins of the book left a significant imprint on itsstyle. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs." He concludes, "As a rule, only those proofs (or sketches of proofs) that are interesting per se and have importantgeneralizations are presented."