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. 1978 edition..
Moreover, it gives the instructor the flexibility to design his own course while providing students with a wealth of historically and mathematically significant examples.
This revised and expanded second edition will be especially useful as a course supplement and reference work for students of general topology.
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.
In addition, discussions of general methods of constructing and changing examples acquaint readers with the art of constructing counterexamples.
Over 25 Venn diagrams and reference charts summarize the properties of the examples and allow students to scan quickly for examples with prescribed properties.
Each example is treated as a whole, with a highly geometric exposition that helps readers comprehend the material.
Ranging from the familiar to the obscure, the examples are preceded by a succinct exposition of general Topology and basic terminology and theory.
Far from presenting all relevant examples, however, the book instead provides a fruitful context in which to ask new questions and seek new answers.
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.
It is only as a result of pursuing the details of each example that students experience a significant increment in topological understanding.
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
