A topological group is a topological space $G$ that is also a group such that the binary operation on the group and the inverse map are both continuous. That is, the two maps \(\cdot:G\times G\to G \text{ given by } (x,y)\mapsto xy\)\(\text{inv}:G\to G \text{ given by } x\mapsto x^{-1}\) are both continuous where $G\times G$ is given the product topology.
Wikidata ID: Q1046291