Perhaps it bears noting that, given a commutative topological ring $R$, the group $R^\times$ of units has natural topology given by the subspace topology under the imbedding $x\to (x,x^{-1})\in R\times R$. In particular, this is the coarsest that makes inversion continuous, etc.

But, yes, this style of characterization was not the norm in those days.

Perhaps it bears noting that, given a commutative topological ring $R$, the group $R^\times$ of units has natural topology given by the subspace topology under the imbedding $x\to (x,x^{-1})\in R\times R$. In particular, this is the coarsest that makes inversion continuous, etc.

(And from the adeles to the ideles this gives the correct topology, unsurprisingly.)

But, yes, this style of characterization was not the norm in those days.