A Geometric Introduction to Topology


Author: Charles Terence Clegg Wall
Publisher: Courier Corporation
ISBN: 0486678504
Category: Mathematics
Page: 168
View: 9144

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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.

An Introduction to Algebraic Topology


Author: Andrew H. Wallace
Publisher: Courier Corporation
ISBN: 0486152952
Category: Mathematics
Page: 208
View: 6188

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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.

A Combinatorial Introduction to Topology


Author: Michael Henle
Publisher: Courier Corporation
ISBN: 9780486679662
Category: Mathematics
Page: 310
View: 4915

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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.

Geometry: A Comprehensive Course


Author: Dan Pedoe
Publisher: Courier Corporation
ISBN: 0486131734
Category: Mathematics
Page: 464
View: 9548

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Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Introduction to Topology

Third Edition
Author: Bert Mendelson
Publisher: Courier Corporation
ISBN: 0486135098
Category: Mathematics
Page: 224
View: 3446

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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 and Geometry for Physicists


Author: Charles Nash,Siddhartha Sen
Publisher: Courier Corporation
ISBN: 0486318362
Category: Mathematics
Page: 320
View: 6582

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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.

Topology

An Introduction with Application to Topological Groups
Author: George McCarty
Publisher: Courier Corporation
ISBN: 0486450821
Category: Mathematics
Page: 288
View: 2829

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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.

From Geometry to Topology


Author: H. Graham Flegg
Publisher: Courier Corporation
ISBN: 0486138496
Category: Mathematics
Page: 208
View: 7707

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Introductory text for first-year math students uses intuitive approach, bridges the gap from familiar concepts of geometry to topology. Exercises and Problems. Includes 101 black-and-white illustrations. 1974 edition.

Topology


Author: John G. Hocking,Gail S. Young
Publisher: Courier Corporation
ISBN: 0486141098
Category: Mathematics
Page: 384
View: 5953

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

Elements of Point Set Topology


Author: John D. Baum
Publisher: Courier Corporation
ISBN: 0486668266
Category: Mathematics
Page: 150
View: 5720

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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.

Principles of Topology


Author: Fred H. Croom
Publisher: Courier Dover Publications
ISBN: 0486801543
Category: Mathematics
Page: 336
View: 6429

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

College Geometry

An Introduction to the Modern Geometry of the Triangle and the Circle
Author: Nathan Altshiller-Court
Publisher: Courier Corporation
ISBN: 0486141373
Category: Mathematics
Page: 336
View: 2244

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The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.

Intuitive Concepts in Elementary Topology


Author: B.H. Arnold
Publisher: Courier Corporation
ISBN: 0486275760
Category: Mathematics
Page: 192
View: 3705

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Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.

Invitation to Combinatorial Topology


Author: Maurice Fréchet,Ky Fan,Howard Whitley Eves
Publisher: Courier Corporation
ISBN: 9780486427867
Category: Mathematics
Page: 124
View: 5433

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Elementary text, accessible to anyone with a background in high school geometry, covers problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, topological polygons, more. Includes 108 figures. 1967 edition.

Topology

An Introduction to the Point-set and Algebraic Areas
Author: Donald W. Kahn
Publisher: Courier Corporation
ISBN: 9780486686097
Category: Mathematics
Page: 217
View: 9735

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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.

Elementary Concepts of Topology


Author: Paul Alexandroff
Publisher: Courier Corporation
ISBN: 0486155064
Category: Mathematics
Page: 64
View: 3255

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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.

Combinatorial Topology


Author: Pavel S. Aleksandrov
Publisher: Courier Corporation
ISBN: 9780486401799
Category: Mathematics
Page: 148
View: 4407

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Clearly written, well-organized, 3-part text begins by dealing with certain classic problems without using the formal techniques of homology theory and advances to the central concept, the Betti groups. Numerous detailed examples.

Introduction to Topology

Second Edition
Author: Theodore W. Gamelin,Robert Everist Greene
Publisher: Courier Corporation
ISBN: 0486320189
Category: Mathematics
Page: 256
View: 4236

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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.

Foundations of Combinatorial Topology


Author: L. S. Pontryagin
Publisher: Courier Dover Publications
ISBN: 0486803252
Category: Mathematics
Page: 112
View: 8902

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Hailed by The Mathematical Gazette as "an extremely valuable addition to the literature of algebraic topology," this concise but rigorous introductory treatment focuses on applications to dimension theory and fixed-point theorems. The lucid text examines complexes and their Betti groups, including Euclidean space, application to dimension theory, and decomposition into components; invariance of the Betti groups, with consideration of the cone construction and barycentric subdivisions of a complex; and continuous mappings and fixed points. Proofs are presented in a complete, careful, and elegant manner. In addition to its value as a one-semester text for graduate-level courses, this volume can also be used as a reference in preparing for seminars or examinations and as a source of basic information on combinatorial topology. Although considerable mathematical maturity is required of readers, formal prerequisites are merely a few simple facts about functions of a real variable, matrices, and commutative groups.

Elementary Topology


Author: Michael C. Gemignani
Publisher: Courier Corporation
ISBN: 9780486665221
Category: Mathematics
Page: 270
View: 9834

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Topology is one of the most rapidly expanding areas of mathematical thought: while its roots are in geometry and analysis, topology now serves as a powerful tool in almost every sphere of mathematical study. This book is intended as a first text in topology, accessible to readers with at least three semesters of a calculus and analytic geometry sequence. In addition to superb coverage of the fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory, and other essentials, Elementary Topology gives added perspective as the author demonstrates how abstract topological notions developed from classical mathematics. For this second edition, numerous exercises have been added as well as a section dealing with paracompactness and complete regularity. The Appendix on infinite products has been extended to include the general Tychonoff theorem; a proof of the Tychonoff theorem which does not depend on the theory of convergence has also been added in Chapter 7.