Undergraduate Topology

Author: Robert H. Kasriel

Publisher: N.A

ISBN: 9780486474199

Category: Mathematics

Page: 285

View: 9433

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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.
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Principles of Topology

Author: Fred H. Croom

Publisher: Courier Dover Publications

ISBN: 0486801543

Category: Mathematics

Page: 336

View: 794

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

Author: Stephen Willard

Publisher: Courier Corporation

ISBN: 0486131785

Category: Mathematics

Page: 384

View: 1468

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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.
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Introduction to Topology

Third Edition

Author: Bert Mendelson

Publisher: Courier Corporation

ISBN: 0486135098

Category: Mathematics

Page: 224

View: 1284

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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.
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Algebraic Topology

Homology and Cohomology

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486462390

Category: Mathematics

Page: 272

View: 722

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Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.
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Elements of Point Set Topology

Author: John D. Baum

Publisher: Courier Corporation

ISBN: 0486668266

Category: Mathematics

Page: 150

View: 1474

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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.
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Introduction to Topological Groups

Author: Taqdir Husain

Publisher: Courier Dover Publications

ISBN: 0486819191

Category: Mathematics

Page: 224

View: 3507

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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.
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A Combinatorial Introduction to Topology

Author: Michael Henle

Publisher: Courier Corporation

ISBN: 9780486679662

Category: Mathematics

Page: 310

View: 802

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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.
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Algebraic Topology

Author: C. R. F. Maunder

Publisher: Courier Corporation

ISBN: 9780486691312

Category: Mathematics

Page: 375

View: 3311

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Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.
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Counterexamples in Topology

Author: Lynn Arthur Steen,J. Arthur Seebach

Publisher: Courier Corporation

ISBN: 0486319296

Category: Mathematics

Page: 272

View: 9888

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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.
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