Definition:Topological Group/Definition 2

Definition
Let $\left({G, \circ}\right)$ be a group.

On its underlying set $G$, let $\left({G, \tau}\right)$ be a topological space.

Let the mapping $\psi: \left({G, \tau}\right) \times \left({G, \tau}\right) \to \left({G, \tau}\right)$ be defined as:
 * $\psi \left({x, y}\right) = x \circ y^{-1}$

Then $\left({G, \circ, \tau}\right)$ is a topological group iff:
 * $\psi$ is a continuous mapping

where $\left({G, \tau}\right) \times \left({G, \tau}\right)$ is considered as $G \times G$ with the product topology.