Introduction to Topology and Geometry

Summary

A concise and unified introduction to the foundational concepts of modern topology and geometryTopology and geometry are branches of mathematics with applications in fields ranging from physics and chemistry to computer science and economics. This textbook offers a rigorous yet accessible approach to the subject that integrates key concepts while providing a robust toolkit that can serve as a starting point for further specialization in diverse areas. It builds intuition by first exploring metric spaces and identifying which properties are topological-that is, unchanged by continuous transformations-and goes on to discuss topological spaces, topological manifolds, simplicial complexes, smooth manifolds, and Riemannian manifolds. Richly illustrated to encourage students to think visually, Introduction to Topology and Geometry is an essential introduction for advanced undergraduates and beginning graduate students in mathematics and related disciplines.