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Principles of Topology

Principles of Topology Author Fred H. Croom
ISBN-10 9780486801544
Release 2016-02-17
Pages 336
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Designed for a one-semester introductory course, this text covers metric spaces, general topological spaces, continuity, topological equivalence, basis and subbasis, connectedness and compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces. 1989 edition.


Topology Author John G. Hocking
ISBN-10 9780486141091
Release 2012-05-23
Pages 384
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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.

Introduction to Topology

Introduction to Topology Author Theodore W. Gamelin
ISBN-10 9780486320182
Release 2013-04-22
Pages 256
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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.

Basic Concepts of Algebraic Topology

Basic Concepts of Algebraic Topology Author F.H. Croom
ISBN-10 9781468494754
Release 2012-12-06
Pages 180
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This text is intended as a one semester introduction to algebraic topology at the undergraduate and beginning graduate levels. Basically, it covers simplicial homology theory, the fundamental group, covering spaces, the higher homotopy groups and introductory singular homology theory. The text follows a broad historical outline and uses the proofs of the discoverers of the important theorems when this is consistent with the elementary level of the course. This method of presentation is intended to reduce the abstract nature of algebraic topology to a level that is palatable for the beginning student and to provide motivation and cohesion that are often lacking in abstact treatments. The text emphasizes the geometric approach to algebraic topology and attempts to show the importance of topological concepts by applying them to problems of geometry and analysis. The prerequisites for this course are calculus at the sophomore level, a one semester introduction to the theory of groups, a one semester introduc tion to point-set topology and some familiarity with vector spaces. Outlines of the prerequisite material can be found in the appendices at the end of the text. It is suggested that the reader not spend time initially working on the appendices, but rather that he read from the beginning of the text, referring to the appendices as his memory needs refreshing. The text is designed for use by college juniors of normal intelligence and does not require "mathematical maturity" beyond the junior level.

Experiments in Topology

Experiments in Topology Author Stephen Barr
ISBN-10 9780486152745
Release 2012-12-04
Pages 210
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Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.


Topology Author Donald W. Kahn
ISBN-10 0486686094
Release 1975
Pages 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.

Undergraduate Topology

Undergraduate Topology Author Robert H. Kasriel
ISBN-10 0486474194
Release 2009-01-01
Pages 285
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General topology offers a valuable tool to students of mathematics, particularly in courses involving complex, real, and functional analysis. This introductory treatment is essentially self-contained, and it features explanations and proofs that relate to every practical aspect of point-set topology. It will prove valuable to undergraduate mathematics majors as well as to graduate students and professionals pursuing mathematics research. Author Robert H. Kasriel, who taught at Georgia Tech for many years, begins with reviews of elementary set theory and Euclidean n-space. The following chapters offer detailed studies of metric spaces and applications to analysis. A survey of general topological spaces and mappings includes considerations of compactness, connectedness, quotient spaces, net and filter convergence, and product spaces. Nearly every one of the 112 sections in this book concludes with a set of exercises that reinforce materials already covered and prepare students for subsequent chapters.

A Combinatorial Introduction to Topology

A Combinatorial Introduction to Topology Author Michael Henle
ISBN-10 0486679667
Release 1979
Pages 310
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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.

General Topology

General Topology Author Stephen Willard
ISBN-10 9780486131788
Release 2012-07-12
Pages 384
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Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.

General Topology

General Topology Author John L. Kelley
ISBN-10 9780486815442
Release 2017-03-15
Pages 320
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"The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure," noted the Bulletin of the American Mathematical Society upon the 1955 publication of John L. Kelley's General Topology. This comprehensive treatment for beginning graduate-level students immediately found a significant audience, and it remains a highly worthwhile and relevant book for students of topology and for professionals in many areas. A systematic exposition of the part of general topology that has proven useful in several branches of mathematics, this volume is especially intended as background for modern analysis. An extensive preliminary chapter presents mathematical foundations for the main text. Subsequent chapters explore topological spaces, the Moore-Smith convergence, product and quotient spaces, embedding and metrization, and compact, uniform, and function spaces. Each chapter concludes with an abundance of problems, which form integral parts of the discussion as well as reinforcements and counter examples that mark the boundaries of possible theorems. The book concludes with an extensive index that provides supplementary material on elementary set theory.

Topological Spaces

Topological Spaces Author Gerard Buskes
ISBN-10 0387949941
Release 1997-08-15
Pages 313
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gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.

Counterexamples in Topology

Counterexamples in Topology Author Lynn Arthur Steen
ISBN-10 9780486319292
Release 2013-04-22
Pages 272
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Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.

Principles and Techniques of Applied Mathematics

Principles and Techniques of Applied Mathematics Author Bernard Friedman
ISBN-10 9780486664446
Release 1956
Pages 315
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Stimulating, thought-provoking study shows how abstract methods of pure mathematics can be used to systematize problem-solving techniques in applied mathematics. Topics include methods for solving integral equations, finding Green’s function for ordinary or partial differential equations, and for finding the spectral representation of ordinary differential operators.

A first course in topology

A first course in topology Author Robert A. Conover
ISBN-10 UOM:49015000695123
Release 1975
Pages 245
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A first course in topology has been writing in one form or another for most of life. You can find so many inspiration from A first course in topology also informative, and entertaining. Click DOWNLOAD or Read Online button to get full A first course in topology book for free.

Introduction to Topology

Introduction to Topology Author Bert Mendelson
ISBN-10 9780486135090
Release 2012-04-26
Pages 224
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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.

Introduction to Analysis

Introduction to Analysis Author Maxwell Rosenlicht
ISBN-10 9780486134680
Release 2012-05-04
Pages 272
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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

Elementary Topology

Elementary Topology Author Michael C. Gemignani
ISBN-10 0486665224
Release 1972
Pages 270
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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.