A First Course In Topology

Author : Robert A Conover
Publisher : Courier Corporation
Page : 276 pages
File Size : 42,6 Mb
Release : 2014-05-21
Category : Mathematics
ISBN : 9780486780016

Get Book

A First Course in Topology by Robert A Conover Pdf

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 www.doverpublications.com

Author : John McCleary
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 44,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821838846

Get Book

A First Course in Topology by John McCleary Pdf

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.

Author : Czes Kosniowski
Publisher : Cambridge University Press
Page : 284 pages
File Size : 48,9 Mb
Release : 1980-09-25
Category : Mathematics
ISBN : 0521231957

Get Book

A First Course in Algebraic Topology by Czes Kosniowski Pdf

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.

Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 51,7 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9780817681227

Get Book

A First Course in Geometric Topology and Differential Geometry by Ethan D. Bloch Pdf

The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.

Author : Marvin J. Greenberg
Publisher : CRC Press
Page : 231 pages
File Size : 51,6 Mb
Release : 2018-03-05
Category : Mathematics
ISBN : 9780429982033

Get Book

Algebraic Topology by Marvin J. Greenberg Pdf

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

Author : William Fulton
Publisher : Springer Science & Business Media
Page : 435 pages
File Size : 54,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461241805

Get Book

Algebraic Topology by William Fulton Pdf

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

Author : James R. Munkres
Publisher : Prentice Hall
Page : 438 pages
File Size : 48,9 Mb
Release : 1974
Category : Mathematics
ISBN : UOM:49015000695883

Get Book

Topology; a First Course by James R. Munkres Pdf

For a one or two semester introduction to topology at the senior or first year graduate level.

Author : William G. Chinn,Norman Earl Steenrod
Publisher : MAA
Page : 170 pages
File Size : 41,6 Mb
Release : 1966
Category : Mathematics
ISBN : 9780883856185

Get Book

First Concepts of Topology by William G. Chinn,Norman Earl Steenrod Pdf

Over 150 problems and solutions.

Author : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 54,7 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821886258

Get Book

Elementary Topology by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov Pdf

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.

Author : John B. Conway
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 54,6 Mb
Release : 2013-11-04
Category : Mathematics
ISBN : 9783319023687

Get Book

A Course in Point Set Topology by John B. Conway Pdf

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.

Author : J. P. May
Publisher : University of Chicago Press
Page : 262 pages
File Size : 42,9 Mb
Release : 1999-09
Category : Mathematics
ISBN : 0226511839

Get Book

A Concise Course in Algebraic Topology by J. P. May Pdf

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.

Author : Tai-Danae Bradley,Tyler Bryson,John Terilla
Publisher : MIT Press
Page : 167 pages
File Size : 50,5 Mb
Release : 2020-08-18
Category : Mathematics
ISBN : 9780262359627

Get Book

Topology by Tai-Danae Bradley,Tyler Bryson,John Terilla Pdf

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.

Author : Mark de Longueville
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 54,7 Mb
Release : 2013
Category : Mathematics
ISBN : 9781441979094

Get Book

A Course in Topological Combinatorics by Mark de Longueville Pdf

This undergraduate textbook in topological combinatorics covers such topics as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. Includes many figures and exercises.

Author : Charles Terence Clegg Wall
Publisher : Courier Corporation
Page : 195 pages
File Size : 46,7 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 9780486678504

Get Book

A Geometric Introduction to Topology by Charles Terence Clegg Wall Pdf

First course in algebraic topology for advanced undergraduates. Homotopy theory, the duality theorem, relation of topological ideas to other branches of pure mathematics. Exercises and problems. 1972 edition.

Author : D. B. Fuks,V. A. Rokhlin
Publisher : Unknown
Page : 519 pages
File Size : 52,9 Mb
Release : 1988
Category : Topology
ISBN : 7506202522

Get Book

Beginner's Course in Topology by D. B. Fuks,V. A. Rokhlin Pdf