 Topological ring

A topological ring is a ring equipped with a topology making addition, additive inversion and multiplication continuous functions. An adic topology is obtained from powers of an ideal.

A **topological ring** is a mathematical structure that combines the concepts of a ring and a topology. Specifically, a topological ring is a ring \( R \) that is also equipped with a topology such that the ring operations (addition and multiplication) are continuous with respect to that topology.