##### Wiktionary

**topological group**

n. (context mathematics English) A group-cum-topological space whose group operations are continuous functions.

##### Wikipedia

**Topological group**

In mathematics, a **topological group** is a group, *G*, together with a topology on *G* such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology. A topological group is a mathematical object with both an algebraic structure and a topological structure. Thus, one may perform algebraic operations, because of the group structure, and one may talk about continuous functions, because of the topology.

Topological groups, along with continuous group actions, are used to study continuous symmetries, which have many applications, for example, in physics.