ENGLISH

Essentials of Topology with Applications

By Steven G. Krantz

Book information

Publisher
Taylor & Francis Group/CRC
Year
2009
ISBN
1420089749, 9781420089745, 9781420089752
Language
english
Format
PDF
Filesize
3 MB (2774212 bytes)
Series
Textbooks in Mathematics
Edition
1st
Pages
xvi,404\422
Orientation
yes
Paginated
no
Scanned
portrait
Time added
2015-04-29 08:29:42

Description

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.

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