Counterexamples in Topology PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Counterexamples in Topology PDF full book. Access full book title Counterexamples in Topology by Lynn Arthur Steen. Download full books in PDF and EPUB format.
Author: Lynn Arthur Steen
Publisher: Courier Corporation
ISBN: 0486319296
Category : Mathematics
Languages : en
Pages : 274
Get Book Here
Book Description
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.
Author: Lynn Arthur Steen
Publisher: Courier Corporation
ISBN: 0486319296
Category : Mathematics
Languages : en
Pages : 274
Get Book Here
Book Description
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.
Author: L.A. Steen
Publisher: Springer Science & Business Media
ISBN: 1461262909
Category : Mathematics
Languages : en
Pages : 249
Get Book Here
Book Description
The creative process of mathematics, both historically and individually, may be described as a counterpoint between theorems and examples. Al though it would be hazardous to claim that the creation of significant examples is less demanding than the development of theory, we have dis covered that focusing on examples is a particularly expeditious means of involving undergraduate mathematics students in actual research. Not only are examples more concrete than theorems-and thus more accessible-but they cut across individual theories and make it both appropriate and neces sary for the student to explore the entire literature in journals as well as texts. Indeed, much of the content of this book was first outlined by under graduate research teams working with the authors at Saint Olaf College during the summers of 1967 and 1968. In compiling and editing material for this book, both the authors and their undergraduate assistants realized a substantial increment in topologi cal insight as a direct result of chasing through details of each example. We hope our readers will have a similar experience. Each of the 143 examples in this book provides innumerable concrete illustrations of definitions, theo rems, and general methods of proof. There is no better way, for instance, to learn what the definition of metacompactness really means than to try to prove that Niemytzki's tangent disc topology is not metacompact. The search for counterexamples is as lively and creative an activity as can be found in mathematics research.
Author: Lynn Arthur Steen
Publisher: Courier Corporation
ISBN: 048668735X
Category : Mathematics
Languages : en
Pages : 274
Get Book Here
Book Description
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.
Author: Bernard R. Gelbaum
Publisher: Courier Corporation
ISBN: 0486134911
Category : Mathematics
Languages : en
Pages : 226
Get Book Here
Book Description
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.
Author: Bernard R. Gelbaum
Publisher: Springer Science & Business Media
ISBN: 1461209935
Category : Mathematics
Languages : en
Pages : 339
Get Book Here
Book Description
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.
Author: Paul Alexandroff
Publisher: Courier Corporation
ISBN: 0486155064
Category : Mathematics
Languages : en
Pages : 68
Get Book Here
Book Description
Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.
Author: S.M. Khaleelulla
Publisher: Springer
ISBN: 3540392688
Category : Mathematics
Languages : en
Pages : 200
Get Book Here
Book Description
Author: Sergiy Klymchuk
Publisher: American Mathematical Soc.
ISBN: 0883857650
Category : Mathematics
Languages : en
Pages : 113
Get Book Here
Book Description
Counterexamples in Calculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses. This book features carefully constructed incorrect mathematical statements that require students to create counterexamples to disprove them. Methods of producing these incorrect statements vary. At times the converse of a well-known theorem is presented. In other instances crucial conditions are omitted or altered or incorrect definitions are employed. Incorrect statements are grouped topically with sections devoted to: Functions, Limits, Continuity, Differential Calculus and Integral Calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool in the study of introductory calculus.
Author: Theodore W. Gamelin
Publisher: Courier Corporation
ISBN: 0486320189
Category : Mathematics
Languages : en
Pages : 258
Get Book Here
Book Description
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.
Author: René L. Schilling
Publisher: Cambridge University Press
ISBN: 1009020390
Category : Mathematics
Languages : en
Pages : 431
Get Book Here
Book Description
Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).
