tag

#groups

2 pages tagged

Maths › 00. General Mathematics ›

04.5 Examples

4.5 Examples: Groups, Spaces, Graphs Structural thinking becomes clearer through examples. This section shows how the same principles appear in different areas. We focus on three domains: groups, topological spaces, and graphs. Each has its own objects, morphisms, invariants, and classification problems. 1. Groups A group is a set $G$ with a binary operation satisfying associativity, identity, and inverses. Objects and maps Objects: groups $(G, \ast)$ Morphisms: group homomorphisms $$...

Maths ›

43. Abstract Harmonic Analysis

This volume extends harmonic analysis to general locally compact groups. It replaces classical Fourier series and transforms with representation-theoretic and measure-theoretic frameworks. Part I. Locally Compact Groups Chapter 1. Topological Groups 1.1 Definitions and examples 1.2 Continuity and group operations 1.3 Subgroups and quotient groups 1.4 Compact and locally compact groups 1.5 Examples Chapter 2. Haar Measure 2.1 Existence and uniqueness 2.2 Left and right invariance 2.3 Integration on groups...