Topology

An Introduction with Application to Topological Groups

Author: George McCarty

Publisher: Courier Corporation

ISBN: 0486450821

Category: Mathematics

Page: 288

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This stimulating introduction employs the language of point set topology to define and discuss topological groups. It examines set-theoretic topology and its applications in function spaces as well as homotopy and the fundamental group. Well-chosen exercises and problems serve as reinforcements. 1967 edition. Includes 99 illustrations.

An Introduction to Algebraic Topology

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486152952

Category: Mathematics

Page: 208

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This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.

Topology

An Introduction to the Point-set and Algebraic Areas

Author: Donald W. Kahn

Publisher: Courier Corporation

ISBN: 9780486686097

Category: Mathematics

Page: 217

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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 Topological Groups

Author: Taqdir Husain

Publisher: Courier Dover Publications

ISBN: 0486819191

Category: Mathematics

Page: 240

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Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.

Elementary Concepts of Topology

Author: Paul Alexandroff

Publisher: Courier Corporation

ISBN: 0486155064

Category: Mathematics

Page: 64

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Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.

A Geometric Introduction to Topology

Author: Charles Terence Clegg Wall

Publisher: Courier Corporation

ISBN: 0486678504

Category: Mathematics

Page: 168

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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.

A Combinatorial Introduction to Topology

Author: Michael Henle

Publisher: Courier Corporation

ISBN: 9780486679662

Category: Mathematics

Page: 310

View: 1848

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Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

Topological Transformation Groups

Author: Deane Montgomery,Leo Zippin

Publisher: Courier Dover Publications

ISBN: 0486831582

Category: Mathematics

Page: 304

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An advanced monograph on the subject of topological transformation groups, this volume summarizes important research conducted during a period of lively activity in this area of mathematics. The book is of particular note because it represents the culmination of research by authors Deane Montgomery and Leo Zippin, undertaken in collaboration with Andrew Gleason of Harvard University, that led to their solution of a well-known mathematical conjecture, Hilbert's Fifth Problem. The treatment begins with an examination of topological spaces and groups and proceeds to locally compact groups and groups with no small subgroups. Subsequent chapters address approximation by Lie groups and transformation groups, concluding with an exploration of compact transformation groups.

Topology for Analysis

Author: Albert Wilansky

Publisher: Courier Corporation

ISBN: 0486469034

Category: Mathematics

Page: 383

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Starting with the first principles of topology, this volume advances to general analysis. Three levels of examples and problems make it appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important concepts, and a 40-page appendix includes tables of theorems and counterexamples. 1970 edition.

Topology and Geometry for Physicists

Author: Charles Nash,Siddhartha Sen

Publisher: Courier Corporation

ISBN: 0486318362

Category: Mathematics

Page: 320

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Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. "Thoroughly recommended" by The Physics Bulletin, this volume's physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.

Introductory Real Analysis

Author: A. N. Kolmogorov,S. V. Fomin

Publisher: Courier Corporation

ISBN: 0486134741

Category: Mathematics

Page: 416

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Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.

Classical Topology and Combinatorial Group Theory

Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 1461243726

Category: Mathematics

Page: 336

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In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.

Graph Theory and Its Applications

Author: Jonathan L. Gross,Jay Yellen,Mark Anderson

Publisher: CRC Press

ISBN: 0429757085

Category: Computers

Page: 577

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Graph Theory and Its Applications, Third Edition is the latest edition of the international, bestselling textbook for undergraduate courses in graph theory, yet it is expansive enough to be used for graduate courses as well. The textbook takes a comprehensive, accessible approach to graph theory, integrating careful exposition of classical developments with emerging methods, models, and practical needs. The authors’ unparalleled treatment is an ideal text for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology. Features of the Third Edition Expanded coverage on several topics (e.g., applications of graph coloring and tree-decompositions) Provides better coverage of algorithms and algebraic and topological graph theory than any other text Incorporates several levels of carefully designed exercises that promote student retention and develop and sharpen problem-solving skills Includes supplementary exercises to develop problem-solving skills, solutions and hints, and a detailed appendix, which reviews the textbook’s topics About the Authors Jonathan L. Gross is a professor of computer science at Columbia University. His research interests include topology and graph theory. Jay Yellen is a professor of mathematics at Rollins College. His current areas of research include graph theory, combinatorics, and algorithms. Mark Anderson is also a mathematics professor at Rollins College. His research interest in graph theory centers on the topological or algebraic side.

Differential Geometric Structures

Author: Walter A. Poor

Publisher: Courier Corporation

ISBN: 0486151913

Category: Mathematics

Page: 352

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This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.

Elements of Point Set Topology

Author: John D. Baum

Publisher: Courier Corporation

ISBN: 0486668266

Category: Mathematics

Page: 150

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Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

A First Course in Topology

An Introduction to Mathematical Thinking

Author: Robert A Conover

Publisher: Courier Corporation

ISBN: 0486780015

Category: Mathematics

Page: 272

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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

First Concepts of Topology

Author: William G. Chinn,Norman Earl Steenrod

Publisher: MAA

ISBN: 9780883856185

Category: Mathematics

Page: 160

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Presents topology as a unifying force for larger areas of mathematics through its application in existence theorems.

Principles of Topology

Author: Fred H. Croom

Publisher: Courier Dover Publications

ISBN: 0486801543

Category: Mathematics

Page: 336

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

Differential Manifolds

Author: Antoni A. Kosinski

Publisher: Courier Corporation

ISBN: 048631815X

Category: Mathematics

Page: 288

View: 8297

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Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.

Introduction to Topology

Second Edition

Author: Theodore W. Gamelin,Robert Everist Greene

Publisher: Courier Corporation

ISBN: 0486320189

Category: Mathematics

Page: 256

View: 8078

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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.