Compactly generated LC-groups, also known as locally compact groups, are a class of mathematical structures that combine topological and algebraic properties. They arise in various areas of mathematics, particularly in the study of topological groups and harmonic analysis. The concept of compact generation plays a fundamental role in understanding the structure and behavior of these groups.
In the mathematical perspective, a compactly generated LC-group is a locally compact group that can be generated by a compact subset. This means that the group can be formed by taking nite products, inverses, and limits of elements in the compact subset. The compact generation property provides important information about the structure and topology of the group.
One of the key features of compactly generated LC-groups is their connection to topological properties. The compact generation property ensures that the group has a well-behaved topological structure, making it amenable to various analytical and topological techniques. Compact generation allows for the study of convergence, continuity, and other important topological properties within the group.
