Counterexamples in Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Counterexamples in Topology write by Lynn Arthur Steen. This book was released on 2013-04-22. Counterexamples in Topology available in PDF, EPUB and Kindle. 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 Topology
Counterexamples in Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Counterexamples in Topology write by L.A. Steen. This book was released on 2012-12-06. Counterexamples in Topology available in PDF, EPUB and Kindle. 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.
Counterexamples in Topology
Counterexamples in Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Counterexamples in Topology write by Lynn Arthur Steen. This book was released on 1995-01-01. Counterexamples in Topology available in PDF, EPUB and Kindle. 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
Counterexamples in Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Counterexamples in Analysis write by Bernard R. Gelbaum. This book was released on 2012-07-12. Counterexamples in Analysis available in PDF, EPUB and Kindle. 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.
Theorems and Counterexamples in Mathematics
Theorems and Counterexamples in Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Theorems and Counterexamples in Mathematics write by Bernard R. Gelbaum. This book was released on 2012-12-06. Theorems and Counterexamples in Mathematics available in PDF, EPUB and Kindle. 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.
