Definition 85.4.8. Let $A$ be a linearly topologized ring.
An element $f \in A$ is called topologically nilpotent if $f^ n \to 0$ as $n \to \infty $.
A weak ideal of definition for $A$ is an open ideal $I \subset A$ consisting entirely of topologically nilpotent elements.
We say $A$ is weakly pre-admissible if $A$ has a weak ideal of definition.
We say $A$ is weakly admissible if $A$ is weakly pre-admissible and complete1.