Essentials of Topology with Applications

Supported by many examples in mathematics, physics, economics, engineering, and other disciplines, this text 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. The text includes a thorough treatment of algebraic topology and contains material on graph theory and dynamical systems, both of which are insightful applications of topological ideas.