Definition:Topological Ring

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


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.