Essentials of Topology with Applications

Steven G. Krantz (Washington University, St. Louis, Missouri, USA)

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Hardback

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English

Chapman & Hall/CRC
28 July 2009

Calculus & mathematical analysis

Series: Textbooks in Mathematics

Brings Readers Up to Speed in This Important and Rapidly Growing Area Supported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological space, open and closed sets, separation axioms, and more, along with applications of the ideas in Morse, manifold, homotopy, and homology theories.

After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory. He also explores meaningful applications in a number of areas, including the traveling salesman problem, digital imaging, mathematical economics, and dynamical systems. The appendices offer background material on logic, set theory, the properties of real numbers, the axiom of choice, and basic algebraic structures.

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.

By: Steven G. Krantz (Washington University St. Louis Missouri USA)
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm,
Weight: 940g
ISBN: 9781420089745
ISBN 10: 1420089749
Series: Textbooks in Mathematics
Pages: 420
Publication Date: 28 July 2009
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

Fundamentals. Advanced Properties of Topological Spaces. Basic Algebraic Topology. Manifold Theory. Moore–Smith Convergence and Nets. Function Spaces. Knot Theory. Graph Theory. Dynamical Systems. Appendices. Solutions of Selected Exercises. Bibliography. Index.

Steven G. Krantz is a professor in the Department of Mathematics at Washington University in St. Louis, Missouri, USA.