Introductory Topology

Exercises and Solutions

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Author: Mohammed Hichem Mortad

Publisher: World Scientific Publishing Company

ISBN: 9814583839

Category: Mathematics

Page: 260

View: 2958

The book offers a good introduction to topology through solved exercises. It is mainly intended for undergraduate students. Most exercises are given with detailed solutions.

Introductory Topology

Exercises and Solutions

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Author: Mohammed Hichem Mortad

Publisher: World Scientific

ISBN: 9813146958

Category:

Page: N.A

View: 9548

The book offers a good introduction to topology through solved exercises. It is mainly intended for undergraduate students. Most exercises are given with detailed solutions. In the second edition, some significant changes have been made, other than the additional exercises. There are also additional proofs (as exercises) of many results in the old section "What You Need To Know", which has been improved and renamed in the new edition as "Essential Background". Indeed, it has been considerably beefed up as it now includes more remarks and results for readers' convenience. The interesting sections "True or False" and "Tests" have remained as they were, apart from a very few changes.

Introduction to Metric and Topological Spaces

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Author: Wilson A Sutherland

Publisher: Oxford University Press

ISBN: 0191568309

Category: Mathematics

Page: N.A

View: 7368

One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.

An Illustrated Introduction to Topology and Homotopy

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Author: Sasho Kalajdzievski

Publisher: CRC Press

ISBN: 1482220814

Category: Mathematics

Page: 485

View: 9229

An Illustrated Introduction to Topology and Homotopy explores the beauty of topology and homotopy theory in a direct and engaging manner while illustrating the power of the theory through many, often surprising, applications. This self-contained book takes a visual and rigorous approach that incorporates both extensive illustrations and full proofs. The first part of the text covers basic topology, ranging from metric spaces and the axioms of topology through subspaces, product spaces, connectedness, compactness, and separation axioms to Urysohn’s lemma, Tietze’s theorems, and Stone-Čech compactification. Focusing on homotopy, the second part starts with the notions of ambient isotopy, homotopy, and the fundamental group. The book then covers basic combinatorial group theory, the Seifert-van Kampen theorem, knots, and low-dimensional manifolds. The last three chapters discuss the theory of covering spaces, the Borsuk-Ulam theorem, and applications in group theory, including various subgroup theorems. Requiring only some familiarity with group theory, the text includes a large number of figures as well as various examples that show how the theory can be applied. Each section starts with brief historical notes that trace the growth of the subject and ends with a set of exercises.

Topology

An Introduction to the Point-set and Algebraic Areas

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Author: Donald W. Kahn

Publisher: Courier Corporation

ISBN: 9780486686097

Category: Mathematics

Page: 217

View: 6815

Comprehensive coverage of elementary general topology as well as algebraic topology, specifically 2-manifolds, covering spaces and fundamental groups. Problems, with selected solutions. Bibliography. 1975 edition.

Introduction to Topology

Second Edition

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Author: Theodore W. Gamelin,Robert Everist Greene

Publisher: Courier Corporation

ISBN: 0486320189

Category: Mathematics

Page: 256

View: 2612

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.

Elementary Topology

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Author: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov

Publisher: American Mathematical Soc.

ISBN: 9780821886250

Category:

Page: N.A

View: 6672

Principles of Topology

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Author: Fred H. Croom

Publisher: Courier Dover Publications

ISBN: 0486801543

Category: Mathematics

Page: 336

View: 8433

Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.

Introduction to Topology

Third Edition

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Author: Bert Mendelson

Publisher: Courier Corporation

ISBN: 0486135098

Category: Mathematics

Page: 224

View: 2222

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 of Surfaces

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Author: L.Christine Kinsey

Publisher: Springer Science & Business Media

ISBN: 1461208998

Category: Mathematics

Page: 281

View: 5024

" . . . that famous pedagogical method whereby one begins with the general and proceeds to the particular only after the student is too confused to understand even that anymore. " Michael Spivak This text was written as an antidote to topology courses such as Spivak It is meant to provide the student with an experience in geomet describes. ric topology. Traditionally, the only topology an undergraduate might see is point-set topology at a fairly abstract level. The next course the average stu dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature, providing quick access to current research, but not developing any intuition or geometric sense. I have tried in this text to provide the undergraduate with a pragmatic introduction to the field, including a sampling from point-set, geometric, and algebraic topology, and trying not to include anything that the student cannot immediately experience. The exercises are to be considered as an in tegral part of the text and, ideally, should be addressed when they are met, rather than at the end of a block of material. Many of them are quite easy and are intended to give the student practice working with the definitions and digesting the current topic before proceeding. The appendix provides a brief survey of the group theory needed.

Topological Spaces

From Distance to Neighborhood

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Author: Gerard Buskes,Arnoud van Rooij

Publisher: Springer Science & Business Media

ISBN: 1461206650

Category: Mathematics

Page: 313

View: 9596

gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.

Topology

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Author: John G. Hocking,Gail S. Young

Publisher: Courier Corporation

ISBN: 0486141098

Category: Mathematics

Page: 384

View: 6510

Superb one-year course in classical topology. Topological spaces and functions, point-set topology, much more. Examples and problems. Bibliography. Index.

Exercises in Analysis

Part 2: Nonlinear Analysis

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Author: Leszek Gasiński,Nikolaos S. Papageorgiou

Publisher: Springer

ISBN: 3319278177

Category: Mathematics

Page: 1062

View: 9580

This second of two Exercises in Analysis volumes covers problems in five core topics of mathematical analysis: Function Spaces, Nonlinear and Multivalued Maps, Smooth and Nonsmooth Calculus, Degree Theory and Fixed Point Theory, and Variational and Topological Methods. Each of five topics corresponds to a different chapter with inclusion of the basic theory and accompanying main definitions and results,followed by suitable comments and remarks for better understanding of the material. Exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic. This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume.

Introduction to Topology

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Author: Min Yan

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110378167

Category: Mathematics

Page: 249

View: 1828

In this book, author uses knowledge from analysis course as a starting point and gradually builds up more abstract concepts in topology for students. Point set topology and combinatorial topology are arranged in alternating order to alleviate learning pressure and exercises are immersed into discussions. The introduction of a concept is followed by examples immediately, and then followed by relevant exercises to facilitate the learning process.

Convergence Foundations of Topology

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Author: Szymon Dolecki,Frédéric Mynard

Publisher: World Scientific Publishing Company

ISBN: 9814571547

Category: Mathematics

Page: 568

View: 8750

This textbook is an alternative to a classical introductory book in point-set topology. The approach, however, is radically different from the classical one. It is based on convergence rather than on open and closed sets. Convergence of filters is a natural generalization of the basic and well-known concept of convergence of sequences, so that convergence theory is more natural and intuitive to many, perhaps most, students than classical topology. On the other hand, the framework of convergence is easier, more powerful and far-reaching which highlights a need for a theory of convergence in various branches of analysis. Convergence theory for filters is gradually introduced and systematically developed. Topological spaces are presented as a special subclass of convergence spaces of particular interest, but a large part of the material usually developed in a topology textbook is treated in the larger realm of convergence spaces.

Introduction to Topology

Pure and Applied

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Author: Colin Conrad Adams,Robert David Franzosa

Publisher: Prentice Hall

ISBN: N.A

Category: Mathematics

Page: 489

View: 5387

Learn the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics. Introduces topology as an important and fascinating mathematics discipline to retain the readers interest in the subject. Is written in an accessible way for readers to understand the usefulness and importance of the application of topology to other fields. Introduces topology concepts combined with their real-world application to subjects such DNA, heart stimulation, population modeling, cosmology, and computer graphics. Covers topics including knot theory, degree theory, dynamical systems and chaos, graph theory, metric spaces, connectedness, and compactness. A useful reference for readers wanting an intuitive introduction to topology.

Category Theory in Context

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Author: Emily Riehl

Publisher: Courier Dover Publications

ISBN: 0486820807

Category: Mathematics

Page: 272

View: 969

Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Algebraic Topology

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Author: N.A

Publisher: 清华大学出版社有限公司

ISBN: 9787302105886

Category: Algebraic topology

Page: 544

View: 9699

Topology

Point-Set and Geometric

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Author: Paul L. Shick

Publisher: John Wiley & Sons

ISBN: 9781118030585

Category: Mathematics

Page: 296

View: 6331

The essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors. Along with the standard point-set topology topics—connected and path-connected spaces, compact spaces, separation axioms, and metric spaces—Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors with the opportunity to choose which "capstone" best suits his or her students. Topology: Point-Set and Geometric features: A short introduction in each chapter designed to motivate the ideas and place them into an appropriate context Sections with exercise sets ranging in difficulty from easy to fairly challenging Exercises that are very creative in their approaches and work well in a classroom setting A supplemental Web site that contains complete and colorful illustrations of certain objects, several learning modules illustrating complicated topics, and animations of particularly complex proofs