A Guide to Topology is an introduction to basic topology. It covers point-set topology, Moore-Smith convergence and function spaces. It treats continuity, compactness, the separation axioms, connectedness, completeness, the relative topology, the quotient topology, the product topology, and all the other fundamental ideas of the subject. The book is filled with examples and illustrations.
Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too.
2. Advanced Properties of Topological
3. Moore-Smith Convergence and Nets
4. Function Spaces
Table of Notation
About the Author
Steven G. Krantz was born in San Francisco, California and grew up in Redwood City, California. He received his undergraduate degree from the University of California at Santa Cruz and the PhD from Princeton University. Krantz has held faculty positions at UCLA, Princeton University, Penn State University, and Washington University in St. Louis. He is currently Deputy Director of the American Institute of Mathematics.
Krantz has written 160 scholarly papers and over 50 books. At least five of the latter are about aspects of complex analysis. Krantz is the holder of the Chauvenet Prize and the Beckenbach Book Award, both awarded by the Mathematical Association of America. He won the UCLA Alumni Association Distinguished Teaching Award. He is the author of How to Teach Mathematics. He has directed 16 PhD students. Krantz serves on the editorial boards of six journals and is Editor-in-Chief of two.
A Guide to Topology is part of the MAA Guides series. As such, this book is intended to provide an overview of topology for graduate students preparing for qualifying exams. It emphasizes point-set topology, with an eye towards applications in analysis. The book is succinct, but provides many examples that clarify the definitions and the differences among topological spaces. There are relatively few proofs. Those provided illustrate how the definitions are typically used. Continued...
1. A Guide to Complex Variables
2. A Guide to Advanced Real Analysis
3. A Guide to Real Variables
4. A Guide to Topology
5. A Guide to Elementary Number Theory
6. A Guide to Advanced Linear Algebra
7. A Guide to Plane Algebraic Curves
8. A Guide to Groups, Rings, and Fields
9. A Guide to Functional Analysis