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.