A topological ring is a ring $R$ together with a topology on the underlying set where the addition map $+:R\times R\to R$ (given by $+(a,b) = a+b$ for all $a,b\in R$) and the multiplication map $\cdot:R\times R\to R$ (given by $\cdot(a,b)= ab$ for all $a,b\in R$) are both continuous.
Wikidata ID: Q922339