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.

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

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.