A topological group is a topological space GGG 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 ⋅:G×G→G given by (x,y)↦xy\cdot:G\times G\to G \text{ given by } (x,y)\mapsto xy⋅:G×G→G given by (x,y)↦xyinv:G→G given by x↦x−1\text{inv}:G\to G \text{ given by } x\mapsto x^{-1}inv:G→G given by x↦x−1 are both continuous where G×GG\times GG×G is given the product topology.
Wikidata ID: Q1046291