counterexamples in topology dover books on mathematics

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Counterexamples In Topology

Author : Lynn Arthur Steen
ISBN : 9780486319292
Genre : Mathematics
File Size : 49. 12 MB
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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.

Understanding Topology

Author : Shaun V. Ault
ISBN : 9781421424071
Genre : Mathematics
File Size : 23. 86 MB
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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"--

Counterexamples In Analysis

Author : Bernard R. Gelbaum
ISBN : 9780486134918
Genre : Mathematics
File Size : 82. 26 MB
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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.

General Topology

Author : John L. Kelley
ISBN : 9780486820668
Genre : Mathematics
File Size : 68. 32 MB
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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.

Algebraic Topology

Author : C. R. F. Maunder
ISBN : 0486691314
Genre : Mathematics
File Size : 43. 70 MB
Format : PDF
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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.

General Topology

Author : Stephen Willard
ISBN : 0486434796
Genre : Mathematics
File Size : 58. 48 MB
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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.

An Introduction To Lebesgue Integration And Fourier Series

Author : Howard J. Wilcox
ISBN : 0486682935
Genre : Mathematics
File Size : 70. 30 MB
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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.

Counterexamples In Probability

Author : Jordan M. Stoyanov
ISBN : 9780486315935
Genre : Mathematics
File Size : 47. 70 MB
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Most mathematical examples illustrate the truth of a statement; counterexamples demonstrate a statement's falsity. This third edition features the author's revisions and corrections plus a substantial new appendix. 2012 edition.

Topology

Author : Paul Louis Shick
ISBN : 0470096055
Genre : Mathematics
File Size : 30. 60 MB
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The essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors. Along with the standard point-set topology topics-connected and path-connected spaces, compact spaces, separation axioms, and metric spaces-Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors with the opportunity to choose which "capstone" best suits his or her students. Topology: Point-Set and Geometric features: A short introduction in each chapter designed to motivate the ideas and place them into an appropriate context Sections with exercise sets ranging in difficulty from easy to fairly challenging Exercises that are very creative in their approaches and work well in a classroom setting A supplemental Web site that contains complete and colorful illustrations of certain objects, several learning modules illustrating complicated topics, and animations of particularly complex proofs

Topology

Author : John G. Hocking
ISBN : 9780486141091
Genre : Mathematics
File Size : 24. 39 MB
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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.

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