Topological Group

A topological group is a mathematical structure that combines the ideas of topology and group theory. It consists of a group, which is a set equipped with a way to combine elements (like addition or multiplication), and a topology, which is a way to understand continuity and limits. In a topological group, both the group operations (combining elements) and the process of taking limits (the topology) behave nicely together. This means you can think of it as a space where you can smoothly perform group operations while also examining how close or far apart elements are, enabling richer mathematical exploration.