# Definition:Topological Ring

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*This page is about Topological Ring in the context of topology. For other uses, see 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**.

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