**Author**: Charles Terence Clegg Wall

**Publisher:**Courier Corporation

**ISBN:**0486678504

**Category:**Mathematics

**Page:**168

**View:**9144

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# Search Results for: a-geometric-introduction-to-topology-dover-books-on-mathematics

**Author**: Charles Terence Clegg Wall

**Publisher:** Courier Corporation

**ISBN:** 0486678504

**Category:** Mathematics

**Page:** 168

**View:** 9144

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**: Andrew H. Wallace

**Publisher:** Courier Corporation

**ISBN:** 0486152952

**Category:** Mathematics

**Page:** 208

**View:** 6188

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.

**Author**: Michael Henle

**Publisher:** Courier Corporation

**ISBN:** 9780486679662

**Category:** Mathematics

**Page:** 310

**View:** 4915

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.

**Author**: Dan Pedoe

**Publisher:** Courier Corporation

**ISBN:** 0486131734

**Category:** Mathematics

**Page:** 464

**View:** 9548

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.
*Third Edition*

**Author**: Bert Mendelson

**Publisher:** Courier Corporation

**ISBN:** 0486135098

**Category:** Mathematics

**Page:** 224

**View:** 3446

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.

**Author**: Charles Nash,Siddhartha Sen

**Publisher:** Courier Corporation

**ISBN:** 0486318362

**Category:** Mathematics

**Page:** 320

**View:** 6582

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.
*An Introduction with Application to Topological Groups*

**Author**: George McCarty

**Publisher:** Courier Corporation

**ISBN:** 0486450821

**Category:** Mathematics

**Page:** 288

**View:** 2829

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.

**Author**: H. Graham Flegg

**Publisher:** Courier Corporation

**ISBN:** 0486138496

**Category:** Mathematics

**Page:** 208

**View:** 7707

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.

**Author**: John G. Hocking,Gail S. Young

**Publisher:** Courier Corporation

**ISBN:** 0486141098

**Category:** Mathematics

**Page:** 384

**View:** 5953

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

**Author**: John D. Baum

**Publisher:** Courier Corporation

**ISBN:** 0486668266

**Category:** Mathematics

**Page:** 150

**View:** 5720

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.

**Author**: Fred H. Croom

**Publisher:** Courier Dover Publications

**ISBN:** 0486801543

**Category:** Mathematics

**Page:** 336

**View:** 6429

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

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.

**Author**: B.H. Arnold

**Publisher:** Courier Corporation

**ISBN:** 0486275760

**Category:** Mathematics

**Page:** 192

**View:** 3705

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.

**Author**: Maurice Fréchet,Ky Fan,Howard Whitley Eves

**Publisher:** Courier Corporation

**ISBN:** 9780486427867

**Category:** Mathematics

**Page:** 124

**View:** 5433

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.
*An Introduction to the Point-set and Algebraic Areas*

**Author**: Donald W. Kahn

**Publisher:** Courier Corporation

**ISBN:** 9780486686097

**Category:** Mathematics

**Page:** 217

**View:** 9735

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.

**Author**: Paul Alexandroff

**Publisher:** Courier Corporation

**ISBN:** 0486155064

**Category:** Mathematics

**Page:** 64

**View:** 3255

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.

**Author**: Pavel S. Aleksandrov

**Publisher:** Courier Corporation

**ISBN:** 9780486401799

**Category:** Mathematics

**Page:** 148

**View:** 4407

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.
*Second Edition*

**Author**: Theodore W. Gamelin,Robert Everist Greene

**Publisher:** Courier Corporation

**ISBN:** 0486320189

**Category:** Mathematics

**Page:** 256

**View:** 4236

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.

**Author**: L. S. Pontryagin

**Publisher:** Courier Dover Publications

**ISBN:** 0486803252

**Category:** Mathematics

**Page:** 112

**View:** 8902

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.

**Author**: Michael C. Gemignani

**Publisher:** Courier Corporation

**ISBN:** 9780486665221

**Category:** Mathematics

**Page:** 270

**View:** 9834

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.

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