Definition:Topological Ring

Definition
Let $\struct{R, +, \circ}$ be a ring.

Let $\tau$ be a topology over $R$.

Then $\struct{R,+,\circ,\tau}$ is a topological ring :


 * $(1): \quad \struct{R, +, \tau}$ is a topological group


 * $(2): \quad \struct{R, \circ,\tau}$ is a topological semigroup.

Also see

 * Definition:Topological Semigroup
 * Definition:Topological Group
 * Definition:Topological Field


 * Criterion for Ring with Unity to be Topological Ring