Definition:Topological Ring

Definition
Let $\left({R,+,\circ}\right)$ be a ring.

Let $\mathcal T$ be a topology over $R$.

Then $\left({R,+,\circ,\mathcal T}\right)$ is a topological ring iff


 * $\left({R,+,\mathcal T}\right)$ is a topological group and
 * $\circ$ is continuous when considered as a mapping from $G \times G$ to $G$.