Author: James R. Munkres

Publisher: Prentice Hall


Category: Mathematics

Page: 537

View: 6913

This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

A First Course in Topology

Continuity and Dimension

Author: John McCleary

Publisher: American Mathematical Soc.

ISBN: 0821838849

Category: Mathematics

Page: 211

View: 2294

How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introduced by Brouwer, giving shape to a subject whose development dominated the twentieth century. The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time.The goal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension. This text is based on the author's course given at Vassar College and is intended for advanced undergraduate students. It is suitable for a semester-long course on topology for students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study.

Algebraic Topology

A First Course

Author: William Fulton

Publisher: Springer Science & Business Media

ISBN: 1461241804

Category: Mathematics

Page: 430

View: 622

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups

A First Course in Topology

An Introduction to Mathematical Thinking

Author: Robert A Conover

Publisher: Courier Corporation

ISBN: 0486780015

Category: Mathematics

Page: 272

View: 7669

Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at

A First Course in Algebraic Topology

Author: Czes Kosniowski

Publisher: CUP Archive

ISBN: 9780521298643

Category: Mathematics

Page: 269

View: 7168

This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities.

Algebraic Topology

A First Course

Author: Marvin J. Greenberg

Publisher: CRC Press

ISBN: 0429982038

Category: Mathematics

Page: 332

View: 4246

Great first book on algebraic topology. Introduces (co)homology through singular theory.

A First Course in Algebraic Topology

Author: A. Lahiri,B. K. Lahiri

Publisher: Alpha Science Int'l Ltd.

ISBN: 9781842650035

Category: Mathematics

Page: 123

View: 4400

This volume is an introductory text where the subject matter has been presented lucidly so as to help self study by the beginners. New definitions are followed by suitable illustrations and the proofs of the theorems are easily accessible to the readers. Sufficient number of examples have been incorporated to facilitate clear understanding of the concepts. The book starts with the basic notions of category, functors and homotopy of continuous mappings including relative homotopy. Fundamental groups of circles and torus have been treated along with the fundamental group of covering spaces. Simplexes and complexes are presented in detail and two homology theories-simplicial homology and singular homology have been considered along with calculations of some homology groups.

Geometry, Dynamics And Topology Of Foliations: A First Course

Author: Scardua Bruno,Rojas Carlos Arnoldo Morales

Publisher: World Scientific

ISBN: 9813207094

Category: Mathematics

Page: 196

View: 7527

The Geometric Theory of Foliations is one of the fields in Mathematics that gathers several distinct domains: Topology, Dynamical Systems, Differential Topology and Geometry, among others. Its great development has allowed a better comprehension of several phenomena of mathematical and physical nature. Our book contains material dating from the origins of the theory of foliations, from the original works of C Ehresmann and G Reeb, up till modern developments. In a suitable choice of topics we are able to cover material in a coherent way bringing the reader to the heart of recent results in the field. A number of theorems, nowadays considered to be classical, like the Reeb Stability Theorem, Haefliger's Theorem, and Novikov Compact leaf Theorem, are proved in the text. The stability theorem of Thurston and the compact leaf theorem of Plante are also thoroughly proved. Nevertheless, these notes are introductory and cover only a minor part of the basic aspects of the rich theory of foliations.

Algebraic topology

a first course

Author: Max K. Agoston

Publisher: N.A


Category: Mathematics

Page: 360

View: 1231

Elementary Topology

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

Publisher: American Mathematical Soc.

ISBN: 9780821886250


Page: N.A

View: 1944

A Concise Course in Algebraic Topology

Author: J. P. May

Publisher: University of Chicago Press

ISBN: 9780226511832

Category: Mathematics

Page: 243

View: 6586

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

A Course in Topological Combinatorics

Author: Mark de Longueville

Publisher: Springer Science & Business Media

ISBN: 1441979107

Category: Mathematics

Page: 240

View: 342

A Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years with growing applications in math, computer science, and other applied areas. Topological combinatorics is concerned with solutions to combinatorial problems by applying topological tools. In most cases these solutions are very elegant and the connection between combinatorics and topology often arises as an unexpected surprise. The textbook covers topics such as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. The text contains a large number of figures that support the understanding of concepts and proofs. In many cases several alternative proofs for the same result are given, and each chapter ends with a series of exercises. The extensive appendix makes the book completely self-contained. The textbook is well suited for advanced undergraduate or beginning graduate mathematics students. Previous knowledge in topology or graph theory is helpful but not necessary. The text may be used as a basis for a one- or two-semester course as well as a supplementary text for a topology or combinatorics class.

A Taste of Topology

Author: Volker Runde

Publisher: Springer Science & Business Media

ISBN: 9780387257907

Category: Mathematics

Page: 176

View: 9662

Having evolved from Runde’s notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology. In places, Runde’s text treats its material differently to other books on the subject, providing a fresh perspective.

Topology (Classic Version)

Author: James Munkres

Publisher: Math Classics

ISBN: 9780134689517

Category: Mathematics

Page: 560

View: 5523

Originally published in 2000, reissued as part of Pearson's modern classic series.

Topology and Geometry

Author: Glen E. Bredon

Publisher: Springer Science & Business Media

ISBN: 1475768486

Category: Mathematics

Page: 131

View: 6927

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS

A Course in Point Set Topology

Author: John B. Conway

Publisher: Springer Science & Business Media

ISBN: 3319023683

Category: Mathematics

Page: 154

View: 9867

This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.

Principles of Topology

Author: Fred H. Croom

Publisher: Courier Dover Publications

ISBN: 0486801543

Category: Mathematics

Page: 336

View: 7945

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

Algebraic Topology

Author: N.A

Publisher: 清华大学出版社有限公司

ISBN: 9787302105886

Category: Algebraic topology

Page: 544

View: 3065