# 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 if and only if:

$(1): \quad \struct {R, +, \tau}$ is a topological group
$(2): \quad \struct {R, \circ,\tau}$ is a topological semigroup.

## Also see

• Results about topological rings can be found here.