Grupos topológicos

Topological groups are mathematical structures that combine algebra and topology. They are groups equipped with a notion of 'closeness' (topology) such that the group operations—multiplication and taking inverses—are continuous functions. This means you can smoothly move around within the group while respecting its algebraic structure, allowing for study of symmetry, spaces, and continuous transformations in a unified framework. Topological groups are fundamental in areas like analysis, geometry, and mathematical physics, providing a foundation for understanding continuous symmetries and spatial properties.