counterexamples in topology dover books on mathematics

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Counterexamples In Topology

Author : Lynn Arthur Steen
ISBN : 9780486319292
Genre : Mathematics
File Size : 56. 32 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.

Counterexamples In Analysis

Author : Bernard R. Gelbaum
ISBN : 9780486134918
Genre : Mathematics
File Size : 42. 9 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.

Topology

Author : John G. Hocking
ISBN : 9780486141091
Genre : Mathematics
File Size : 41. 48 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.

A Combinatorial Introduction To Topology

Author : Michael Henle
ISBN : 0486679667
Genre : Mathematics
File Size : 81. 48 MB
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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.

Counterexamples In Probability

Author : Jordan M. Stoyanov
ISBN : 9780486499987
Genre : Education
File Size : 67. 9 MB
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"While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statement's falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching and learning. The definitive book on the subject in regards to probability, this third edition features the author's revisions and corrections plus a substantial new appendix. 2013 edition"--

Elements Of Point Set Topology

Author : John D. Baum
ISBN : 9780486668260
Genre : Mathematics
File Size : 65. 11 MB
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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.

General Topology

Author : John L. Kelley
ISBN : 9780486820668
Genre : Mathematics
File Size : 40. 50 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.

Theorems And Counterexamples In Mathematics

Author : Bernard R. Gelbaum
ISBN : 9781461209935
Genre : Mathematics
File Size : 79. 77 MB
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The gratifying response to Counterexamples in analysis (CEA) was followed, when the book went out of print, by expressions of dismay from those who were unable to acquire it. The connection of the present volume with CEA is clear, although the sights here are set higher. In the quarter-century since the appearance of CEA, mathematical education has taken some large steps reflected in both the undergraduate and graduate curricula. What was once taken as very new, remote, or arcane is now a well-established part of mathematical study and discourse. Consequently the approach here is designed to match the observed progress. The contents are intended to provide graduate and ad vanced undergraduate students as well as the general mathematical public with a modern treatment of some theorems and examples that constitute a rounding out and elaboration of the standard parts of algebra, analysis, geometry, logic, probability, set theory, and topology. The items included are presented in the spirit of a conversation among mathematicians who know the language but are interested in some of the ramifications of the subjects with which they routinely deal. Although such an approach might be construed as demanding, there is an extensive GLOSSARY jlNDEX where all but the most familiar notions are clearly defined and explained. The object ofthe body of the text is more to enhance what the reader already knows than to review definitions and notations that have become part of every mathematician's working context.

Counterexamples In Calculus

Author : Sergiy Klymchuk
ISBN : 9780883857656
Genre : Mathematics
File Size : 71. 36 MB
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Originally published: New Zealand: Maths Press, 2004.

Linear Analysis And Representation Theory

Author : Steven A. Gaal
ISBN : 9783642807411
Genre : Mathematics
File Size : 20. 7 MB
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In an age when more and more items. are made to be quickly disposable or soon become obsolete due to either progress or other man caused reasons it seems almost anachronistic to write a book in the classical sense. A mathematics book becomes an indespensible companion, if it is worthy of such a relation, not by being rapidly read from cover to cover but by frequent browsing, consultation and other occasional use. While trying to create such a work I tried not to be encyclopedic but rather select only those parts of each chosen topic which I could present clearly and accurately in a formulation which is likely to last. The material I chose is all mathematics which is interesting and important both for the mathematician and to a large extent also for the mathematical physicist. I regret that at present I could not give a similar account on direct integrals and the representation theory of certain classes of Lie groups. I carefully kept the level of presentation throughout the whole book as uniform as possible. Certain introductory sections are kept shorter and are perhaps slightly more detailed in order to help the newcomer prog ress with it at the same rate as the more experienced person is going to proceed with his study of the details.

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