Counterexamples in Topology

Author: Lynn Arthur Steen,J. Arthur Seebach

Publisher: Courier Corporation

ISBN: 0486319296

Category: Mathematics

Page: 272

View: 9133

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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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Understanding Topology

A Practical Introduction

Author: Shaun V. Ault

Publisher: JHU Press

ISBN: 142142407X

Category: Mathematics

Page: 416

View: 9733

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"Topology can present significant challenges for undergraduate students of mathematics and the sciences. 'Understanding topology' aims to change that. The perfect introductory topology textbook, 'Understanding topology' requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from chemical dynamics to determining the shape of the universe, will engage students in a way traditional topology textbooks do not"--
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Counterexamples in Analysis

Author: Bernard R. Gelbaum,John M. H. Olmsted

Publisher: Courier Corporation

ISBN: 0486134911

Category: Mathematics

Page: 224

View: 8722

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These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
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General Topology

Author: Stephen Willard

Publisher: Courier Corporation

ISBN: 9780486434797

Category: Mathematics

Page: 369

View: 3882

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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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General Topology

Author: John L. Kelley

Publisher: Courier Dover Publications

ISBN: 0486820661

Category: Mathematics

Page: 320

View: 9008

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Comprehensive text for beginning graduate-level students and professionals. "The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure." — Bulletin of the American Mathematical Society. 1955 edition.
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Algebraic Topology

Author: C. R. F. Maunder

Publisher: Courier Corporation

ISBN: 9780486691312

Category: Mathematics

Page: 375

View: 3970

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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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Function Spaces with Uniform, Fine and Graph Topologies

Author: Robert A. McCoy,Subiman Kundu,Varun Jindal

Publisher: Springer

ISBN: 3319770543

Category: Mathematics

Page: 106

View: 5105

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This book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to give generalizations wherever possible, enriching the existing literature. The goal of this monograph is to provide an extensive study of the uniform, fine and graph topologies on the space C(X,Y) of all continuous functions from a Tychonoff space X to a metric space (Y,d); and the uniform and fine topologies on the space H(X) of all self-homeomorphisms on a metric space (X,d). The subject matter of this monograph is significant from the theoretical viewpoint, but also has applications in areas such as analysis, approximation theory and differential topology. Written in an accessible style, this book will be of interest to researchers as well as graduate students in this vibrant research area.
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An Introduction to Lebesgue Integration and Fourier Series

Author: Howard J. Wilcox,David L. Myers

Publisher: Courier Corporation

ISBN: 9780486682938

Category: Mathematics

Page: 159

View: 3442

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This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.
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Topological Uniform Structures

Author: Warren Page

Publisher: Courier Dover Publications

ISBN: 9780486658087

Category: Mathematics

Page: 398

View: 7473

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Exceptionally smooth, clear, detailed examination of uniform spaces, topological groups, topological vector spaces, topological algebras and abstract harmonic analysis. Also, topological vector-valued measure spaces as well as numerous problems and examples. For advanced undergraduates and beginning graduate students. Bibliography. Index.
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Topology for Analysis

Author: Albert Wilansky

Publisher: Courier Corporation

ISBN: 0486469034

Category: Mathematics

Page: 383

View: 3895

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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.
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