Definition:Topological Ring

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