Lynn Arthur Steen J. Arthur Seebach
- Title: Counterexamples in Topology
- Author: Lynn Arthur Steen J. Arthur Seebach
- ISBN: 9780486687353
- Page: 236
- Format: Paperback
Counterexamples in Topology Dover Books on Mathematics According to the authors of this highly useful compendium, focusing on examples is an extremely effective method of involving undergraduate mathematics students in actual research. Counterexamples in Analysis Dover Books on Mathematics These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as real variables, starting at the level of calculus. General topology In mathematics, general topology is the branch of topology that deals with the basic set theoretic definitions and constructions used in topology It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology.Another name for general topology is point set topology. The fundamental concepts in point set topology are Introduction to Topology Second Edition Dover Publications One of the most important milestones in mathematics in the twentieth century was the development of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics While there are many other works on introductory topology, this Topological space In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods The definition of a topological space relies only upon set theory and is the most general notion of a mathematical space that allows for the definition of concepts such as JSTOR Viewing Subject Mathematics JSTOR is part of ITHAKA, a not for profit organization helping the academic community use digital technologies to preserve the scholarly record and to advance research and teaching in sustainable ways. Mathematical Association of America on JSTOR JSTOR is part of ITHAKA, a not for profit organization helping the academic community use digital technologies to preserve the scholarly record and to advance research and teaching in sustainable ways. The Greatest Mathematicians fabpedigree The Hundred Greatest Mathematicians of the Past This is the long page, with list and biographies Click here for just the List, with links to the biographies.Or Click here for a How to Do Mathematical Research University of Hawaii Each vector in this sequence is the preceding vector The fact that there is an infinite sequence of vectors determines the shape of the group. Ward Whitt Publications Publications Weak Convergence Theorems for Queues in Heavy Traffic, Ph.D thesis, Cornell University Committee Donald L Iglehart Principal Advisor , H
According to the authors of this highly useful compendium, focusing on examples is an extremely effective method of involving undergraduate mathematics students in actual research It is only as a result of pursuing the details of each example that students experience a significant increment in topological understanding With that in mind, Professors Steen and Seebach haveAccording to the authors of this highly useful compendium, focusing on examples is an extremely effective method of involving undergraduate mathematics students in actual research It is only as a result of pursuing the details of each example that students experience a significant increment in topological understanding With that in mind, Professors Steen and Seebach have assembled 143 examples in this book, providing innumerable concrete illustrations of definitions, theorems, and general methods of proof Far from presenting all relevant examples, however, the book instead provides a fruitful context in which to ask new questions and seek new answers.Ranging from the familiar to the obscure, the examples are preceded by a succinct exposition of general topology and basic terminology and theory Each example is treated as a whole, with a highly geometric exposition that helps readers comprehend the material Over 25 Venn diagrams and reference charts summarize the properties of the examples and allow students to scan quickly for examples with prescribed properties In addition, discussions of general methods of constructing and changing examples acquaint readers with the art of constructing counterexamples The authors have included an extensive collection of problems and exercises, all correlated with various examples, and a bibliography of 140 sources, tracing each uncommon example to its origin.This revised and expanded second edition will be especially useful as a course supplement and reference work for students of general topology Moreover, it gives the instructor the flexibility to design his own course while providing students with a wealth of historically and mathematically significant examples 1978 edition.
Recent Comments "Counterexamples in Topology"
A great companion to Munkres to have.[Review 1 - 05/05/17.]
Topology is abstract enough that if you are learning the subject for the first time, and you are not constantly challenging yourself to come up with concrete applications and counterexamples, you will probably learn very little. If you find the requirements of a particular theorem to be a bit over-the-top and find yourself a few brain cells short of coming up with a proper counterexample to illuminate why the theorem is stated in that way, this book will be extremely useful. Even if you can alwa [...]
Every student of topology should have this. Steen and Seebach provide instances to illustrate every distinction commonly made in topology (e.g. regular but not normal, T1 but not Hausdorff). In the latter part of the book the authors offer a thorough discussion of metrizability (under what conditions can a topological space be given a metric that "agrees" with its topology?).
As the title states, this book provides counterexamples in topology (that you were probably too lazy to come up with). Some of the examples were very critical in understanding topology at the undergraduate level, but as one may suspect, most of them were just so esoteric to the point of absurdity.
I might have debated whether to give this 4 or 5 starsif it had been a +$50 math book, but at $10, "the choice(function) is clear "
The Dover "Counterexamples in" line is generally awesome; no exception here.
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