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.
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