Category:Topological Rings

This category contains results about Topological Rings.
Definitions specific to this category can be found in Definitions/Topological Rings.

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.