Overview

This book is an ambitious but optimistic treatment of the subject of topology. Not only does Elements of Topology: Theory and Practice, Second Edition treat the standard basic material on point-set topology, but it also gives an introduction to algebraic topology, a treatment of manifolds, a discussion of function spaces, and some ideas of knot theory. Even the exciting new topic of the Jones polynomial is covered. After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory. Topic coverage has been reduced in this second edition, and exercise sets have been added at the end of each section. The book as a whole—and the first two chapters in particular— offer many examples. Solutions to selected exercises are included at the end. Today’s students need a text that speaks to them in their own language, and at a pace with which they are comfortable. That is the goal of this edition. Taking a fresh and accessible approach to a venerable subject, this text provides excellent representations of topological ideas. It forms the foundation for further mathematical study in real analysis, abstract algebra, and beyond.

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9781041216834

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Steven G. Krantz is a professor at Washington University in St. Louis where he teaches mathematics. He has previously taught at UCLA, Princeton University, and Penn State University. He earned his PhD from Princeton University in 1974. Prof. Krantz has directed 20 PhD students and 8 master's-degree students, and he published over 130 books and over 300 scholarly articles. He is the holder of the Chauvenet Prize, the Beckenbach Book Award, and the Kemper Prize, and he is a fellow of the American Mathematical Society.

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