Lemma 85.4.12. Let $\varphi : A \to B$ be a continuous map of weakly admissible topological rings. The following are equivalent
$\varphi $ is taut,
for every weak ideal of definition $I \subset A$ the closure of $\varphi (I)B$ is a weak ideal of definition of $B$ and these form a fundamental system of weak ideals of definition of $B$.