Essentials of Topology with Applications

ISBN-13: 9781138114456 / Angielski / Miękka / 2017 / 420 str.

Steven G. Krantz

Opis

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.

Spis treści

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.

O autorze

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