#lie-groups

22. Topological Groups, Lie Groups

This volume studies groups equipped with topology and smooth structure. It connects algebra, topology, and geometry, with applications in analysis and physics. Part I. Topological Groups Chapter 1. Topological Groups 1.1 Definitions and examples 1.2 Continuity of multiplication and inversion 1.3 Subgroups and quotient groups 1.4 Homomorphisms 1.5 Basic properties Chapter 2. Fundamental Properties 2.1 Compactness 2.2 Connectedness 2.3 Local compactness 2.4 Separation axioms 2.5 Examples Chapter 3. Haar Measure...