COUNTEREXAMPLES IN TOPOLOGY STEEN PDF

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 have assembled 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.

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It seems that you're in Germany. We have a dedicated site for Germany. Authors: Steen , L. The creative process of mathematics, both historically and individually, may be described as a counterpoint between theorems and examples.

We hope our readers will have a similar experience. 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. Only valid for books with an ebook version. Springer Reference Works are not included. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Free Preview. Buy eBook. Buy Softcover. FAQ Policy. About this book The creative process of mathematics, both historically and individually, may be described as a counterpoint between theorems and examples.

Show all. Compactness Pages Steen, Lynn Arthur et al. Connectedness Pages Steen, Lynn Arthur et al. Counterexamples Pages Steen, Lynn Arthur et al. Show next xx. Read this book on SpringerLink.

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Counterexamples in Topology

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 have assembled 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.

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It seems that you're in Germany. We have a dedicated site for Germany. Authors: Steen , L. The creative process of mathematics, both historically and individually, may be described as a counterpoint between theorems and examples. We hope our readers will have a similar experience. 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.

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Counterexamples in Topology , 2nd ed. Arthur Seebach, Jr. In the process of working on problems like the metrization problem , topologists including Steen and Seebach have defined a wide variety of topological properties. It is often useful in the study and understanding of abstracts such as topological spaces to determine that one property does not follow from another.

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